Capablanca and Lasker did play for the world championship in 1921 (after previously failing to come to terms for a potential match in 1911) Cap won 9-5, though I'm sure Lasker was past his prime by then...
http://www.chessgames.com/perl/chess.pl?tid=54111
By 1920, Lasker recognized Capablanca's prowess, and resigned the title to him, saying, "You have earned the title not by the formality of a challenge, but by your brilliant mastery."2 Capablanca, having felt robbed of his chance to win the title in the traditional fashion, convinced Lasker to play, but Lasker did so only on condition that his resignation be accepted, and he be regarded as the challenger. Lasker's resignation was not widely recognized at the time, nor today, therefore this match is generally regarded as the one in which the title changed hands.
In Havana, from March 15 to April 28, 1921, the match took place. Whomever you regard as the challenger, the winner was Capablanca, who prevailed without a single loss, +4 -0 =10. Four games down, with at most 10 more to play, Lasker resigned the match prematurely after Game 14, citing ill health, and Capablanca became the third World Chess Champion.
My first book was written by Lasker in Classical notation. Can't recall the name of it. Was hard for me to follow at my age at the time. Great player, he was, though.