Lasker said anyone can become a master
Can the average person become a chess master?

Lasker said anyone can become a master
Lasker was wrong.
Many elite players have underestimated how hard it is to master their game, not just in chess. Elite golfers often say it'd be easy to become a golf pro, but people who have tried rarely succeed.
Having said that, Lasker was right about the best way to begin to teach a novice: focus on the most basic endgames and work backwards.
"... Lasker was right about the best way to begin to teach a novice: focus on the most basic endgames and work backwards." - SmyslovFan
Chapter two of Lasker's Manual was about the opening.
https://web.archive.org/web/20140708104828/http://www.chesscafe.com/text/review658.pdf
"The initial six chapters [of Lasker's Common Sense in Chess] focus on the opening"
https://web.archive.org/web/20140708085539/http://www.chesscafe.com/text/review268.pdf

In Lasker's Manual of Chess (2008 p. 248), he wrote:
"Let us assume that a master who follows a good method, say, the method of this book, strives to educate a young man ignorant of chess to the level of one who, if conceded any odds, would surely come out the winner. How much time would the teacher need for this achievement? I think that I am correct in making the following calculation:
Rules of Play and Exercises: 5 hrs.
Elementary Endings: 5 hrs.
Some Openings: 10 hrs
Combination: 20 hrs
Position Play: 40 hrs
Play and Analysis: 120 hrs"

Can becoming a chess master be taught to an average person? In other words, is being a chess master nature or nurture? Can it be all nurture?
Yes, chess mastery (2200+ strength) can be taught to an average person. It's just a matter of learning, practice, and reviewing/correcting your mistakes.
The process is entirely possible for the average individual, but it also takes years of work—and the work has to be focused (not random).
There's no such thing as a "natural" chess player—nobody springs out of the womb knowing how to play chess. It's a learned skill.
"... The level at which one plays is governed by a number of vague and poorly understood factors. The first is what one might term 'natural talent'. ..." - GM John Nunn (2006)
"... Lasker was right about the best way to begin to teach a novice: focus on the most basic endgames and work backwards." - SmyslovFan
Chapter two of Lasker's Manual was about the opening.
https://web.archive.org/web/20140708104828/http://www.chesscafe.com/text/review658.pdf
"The initial six chapters [of Lasker's Common Sense in Chess] focus on the opening"
https://web.archive.org/web/20140708085539/http://www.chesscafe.com/text/review268.pdf
Point of fact: Book Two of Lasker's Manual introduces several openings to go over the ideas of those openings. He starts off the book by saying that endgames and "combinations" (his word for tactics) are more important, but understanding the idea behind the first few opening moves can help. It is also the shortest of the 6 books.
With positional play later, he wasn't exactly working backwards, was he?

you need 10,000 hrs of focus practice and study to master some subject
that is a general rule for anybody wanting to be an expert in a field
"... In a recently published issue of the journal 'Intelligence' there were numerous studies, analysis, and pieces on the 10,000hr rule. In particular, one study by David Hambrick and colleagues entitled “Deliberate practice: Is that all it takes to become an expert”, sought out to 'test Ericsson’s claim that "individual differences in ultimate performance can largely be accounted for by differential amounts of past and current levels of practice.' As a refresher, Ericsson was the original researcher who developed and then publicized the concepts, which then took off with Gladwell’s Outliers, Geoffrey Colvin’s Talent is Overrated, Daniel Coyle’s The Talent Code, and numerous others who jumped on the bandwagon with their own spin.
In there research Hambrick reanalyzed 12 studies looking at expert performance in chess and music. Similar to Ericsson’s original work, they simply looked at hours of deliberate practice for each and compared it to performance levels along their development. In the chess studies, they found that deliberate practice explained 34% of the variance in performance, and therefore 66% unexplained. Looking at the individual numbers is even more staggering. There were some people who had over 20,000 hours of deliberate practice yet never went beyond Intermediate, the lowest of the three levels (intermediate, expert, and master). Perhaps most striking, was the range of “masters” was 832 hours to 24,284hrs to reach mastery.
When looking at Music, the results were very similar. 29.9% of the variance in performance was explained by amount of deliberate practice.
The whole study is worth a read as it delves into intelligence, personality, and other factors related to reaching 'expertise.' However, the take away to me is simply common sense. Does practice make you better? Of course it does, but it isn’t the be all end all. And you know what, neither is genetics. ..."
http://www.scienceofrunning.com/2014/03/why-gladwells-10000-rule-is-just-plain.html
"... Lasker was right about the best way to begin to teach a novice: focus on the most basic endgames and work backwards." - SmyslovFan
Chapter two of Lasker's Manual was about the opening.
https://web.archive.org/web/20140708104828/http://www.chesscafe.com/text/review658.pdf
"The initial six chapters [of Lasker's Common Sense in Chess] focus on the opening"
https://web.archive.org/web/20140708085539/http://www.chesscafe.com/text/review268.pdf
Point of fact: Book Two of Lasker's Manual introduces several openings to go over the ideas of those openings. He starts off the book by saying that endgames and "combinations" (his word for tactics) are more important, but understanding the idea behind the first few opening moves can help. It is also the shortest of the 6 books.
With positional play later, he wasn't exactly working backwards, was he?
Again, you must actually read instead of just Googling. He states why he covers openings when he does (basically, to get it out of the way because it is what beginners ask about most often).
"because it is what beginners ask about most often"
Lasker language or BobbyTalparov language?
"... nobody can wholly escape the dire necessity of compiling variations and of examining and memorizing them. And therefore such a compilation is correctly included in a manual of chess." - Lasker's Manual of Chess (algebraic edition)

In Neil Charness's 2005 study, he and his colleagues found the highest correlation between rating and serious solo study. The second most important factor appeared to be the size of the player's library of books and study materials. The age at which the player became serious about chess and the number of hours spent in tournament play since starting also seemed to have some effect on their rating.

So you're asking if anyone can become a chess master?
Haven't you heard the old saying? "Chess masters are about average"?
Well now you know, and because half of people are below average, only half of people can be chess masters.
qed
"... Lasker was right about the best
way to begin to teach a novice: focus
on the most basic endgames and work
backwards." - SmyslovFan
Chapter two of Lasker's Manual was
about the opening.
chesscafe.com/text/review658.pdf
"The initial six chapters [of Lasker's
Common Sense in Chess] focus on
the opening"
Point of fact: Book Two of Lasker's Manual
introduces several openings to go over the
ideas of those openings. He starts off the
book by saying that endgames and
"combinations" (his word for tactics) are
more important, but understanding the idea
behind the first few opening moves can help.
It is also the shortest of the 6 books.
With positional play later, he wasn't exactly
working backwards, was he?
Again, you must actually read instead of just Googling.
He states why he covers openings when he does
(basically, to get it out of the way because it is what
beginners ask about most often).
"because it is what beginners ask about most often"
Lasker language or BobbyTalparov language?
"... nobody can wholly escape the dire necessity of
compiling variations and of examining and memorizing
them. And therefore such a compilation is correctly
included in a manual of chess." - Lasker's Manual of
Chess (algebraic edition)
He literally spends 2 pages explaining what he is doing, and
you (as usual) pick a quote completely out of context. If you
were to actually read book two, you would see he only does
a cursory review of common openings, usually no more than
10 moves with most of them not even containing variations
(the Sicilian is covered in 2 paragraphs). Book Two is
basically the precursor to Silman's "Complete Book of Chess
Strategy" (not surprising since Silman is a huge fan of Lasker).
In the latest contribution, I do not see any reference to "why he covers openings when he does" and "because it is what beginners ask about most often". Are those ideas now being discarded by BobbyTalparov?

To be a master at anything takes more than average. In fact to become master a person decides to sacrifice a lot of things to achieve his goal.

Kindaspongey, I know it's hard to admit when you are wrong. The first book in Manual of Chess covers the basics. After he shows how the pieces move, he starts discussing the basic mates and endgame principles. That's all in book 1 (not chapter one).
Lasker does cover the openings in book 2.
You are wrong about the contents of chapter two of the Manual of Chess, which deals with a "Brief Account of the Origin of Chess".
Lasker doesn't deal with the opening until Book 2.
I am a great talent and my goal is Candidate Master at the age of 93.
Mr Average will have big problems breaking the 2000-line. All 2000 players I know is more than average talented.