-I think you are lucky if your opponent had a bad plan/ or executed his plan badly....this had nothing to do with your skill level.
What is "luck" in chess?

Who was that Ukrainian player who reached 2741 in the live ratings last year due to a spurt, and now totally gone from the Top 100 even?
Luck or sandbagger?
Edit: Found him....http://en.wikipedia.org/wiki/Denis_Khismatullin
Sure if your opponent's mouse slips, or some other unforseeable circumstance, that would be "luck", but otherwise, how does one "get lucky"?
Simple - your opponent makes a game losing mistake and you spot it.

Carlsen blundering in Game 6 of WC was lucky for Anand. Anand missing Carlsen's blunder was lucky for Carlsen.
Anyone who knows the entire game tree of chess and can play an optimal move in any position has "skill" (or possibly merely knowledge).
Anyone who can work out the best posible move (or moves) in any position has "skill".
Everyone else has a greater or lesser degree of "non-skill".
Individual players vary in the "particular skills" they bring to the board.
If, for example, a player knows how to execute the Knight and Bishop Mate from any position (in which it is possible to do so) they have that "particular skill".
I read many years ago that a well known Grand master said "the person that wins the game is the one that made the next to the last mistake". We're not rolling dice. We make moves that have a finite number of possible responses. If you want to call it luck when your opponent make the wrong move, then so be it. In my opinion luck has nothing to do with it.
So what do you call it when you opponent makes the wrong move before you do it? To me it looks like it is luck. There is no way to predict when the mistake will be made - just like when rolling dice.
I agree with what you said to a point. To clarify mine, to me the word luck implies the element of chance which is beyond our control, in that we have no choice in the outcome. When you opponent makes a move, that is his choice, he or she chooses the move. Luck enters in only when the wrong move is made. So you are lucky your opponent made the wrong move. Then luck only appies to the person on the receiving end of the wrong move. The person making the wrong move simply made a bad choice.

I think there is a caveat to a piece or square being protected by luck in a variation that a player did not see in advance.
You could argue that this will happen more often to players who put their pieces and pawns on good squares anyway. So, although it is 'lucky' up to a point, good players on the whole will be 'luckier' in this sense than bad players.

A perfect example of "luck" is:
Carlsen blundering a piece and Anand not take it ...
How else could be called ( avoinding any cospiracy theory)

That just seems like an error on both sides rather than luck to me.
Of course its an error, but you dont expect a world camp hanging a piece, and you dont expect the other to not see that!
How could you not call Carlsen "lucky" that Anand didn't saw his hanging piece.

I often play sharper than my skills. Sometimes I can go on playing ok for a full game or two, and other times I make mistakes. The lucky player is the player playing me when I make mistakes, if he is good enough to spot it and punish it.
So, you need some skills to cash in your luck.
The games where I play at my best, meeting me in these games is bad luck, but not only. I will at the same time highlight something you does wrong, and give you the opportunity to learn.

Luck is when your opponent didn't notice the blunder you made.
Luck is when not only did your opponent blundered....but that you had the eyes to see that he did....
That just seems like an error on both sides rather than luck to me.
How could you not call Carlsen "lucky" that Anand didn't saw his hanging piece.
Because Carlsen and Anand are still human and error prone regardless of how well they play chess in general. Give any human a very difficult task to perform while feeling stress, nerves, etc. and mistakes will happen. I call it "being human" rather than "luck".
And when players say they were lucky, it's usually just a polite way of acknowleding their opponent made an unusual mistake. But a mistake it remains; not an isolated act.

I suppose what we call these things doesn't really matter; it justs seems to me that there is a difference between something that turns out well for you by something you did with unforeseen benefits, and something that turns out well for you through someone else's error.

In fact the word 'luck' is used in many contexts where it may be inappropriate. We say someone is lucky to have a nice job or a great talent for something, when there is a whole background of other stuff that may not be acknowledged.
You could even say that it is at the root of the right wing and left wing political views of life (rich people are hardworking, poor people have only themselves to blame; or rich people are lucky, poor people are the victims of unfortunate circumstances). I like to use the word in its purer form, like being lucky when 36 red comes up when you put your shirt on it, but I may be in a minority.
There is no such thing as luck in chess, minus mouse slips in online. What we perceive as luck are those favourable circumstances we have no control over, which is usually the opponent's imcompetence.
When you play an opponent of equal strength you have both same competence (or incompetence). You have roughly same probability to make a mistake on every move. When your opponent makes mistakes earlier than you or more often or they are more severe - I think it is luck.
Luck - the things that happen to a person because of chance; the accidental way things happen without being planned (Merriam-Webster dictionary)

Magnus Carlsen is the chessplayer with most luck, because he is able to exploit very small luck components and create advantage.
To win against a GM, I need BIG luck, like he blunders away the queen and a rook. Magnus only need small positional lucks, and gets on top.
Magnus gets lots of more luck than me, because he is able to see those tiny luckfragments and exploit them. I too could have the same luck, but my chessvision is to blurry and narrow, so I dont see the luckfragments, and if I saw them, I wouldnt know how to build advantage.
That huge pile of luck that I get, but dont see, doesnt count, because I dont use it. In stead I trow away some dubious moves, handing the luck over to my opponent.
I differentiate between being lucky and benefitting from bad play from my opponnent. If you hang your queen against me from a better position that's lucky. However to me REAL luck in chess is when I execute a plan and then find out that I've got a piece exactly where I need it even though I hadn't moved it to that square with any idea that it would help me out in the way that it has.
Now THAT'S LUCK :)