The London rules only set forth conditions under which a challenger could demand a match. It didn't prevent a champion from accepting challenges under other conditions too.

...Alekhine broke the London Contract by agreeing to play for the championship with Bogo and Euwe for much less. So Alekhine singling out Capablanca for the strictest adherence to original ammount does not seem to have much of a legal basis. Nor can it be realy seen as a principled stance. It was exactly what it was, a fig leaf against the ignominy of backing out of the dangerous rematch commitment.>

Or was it vindictiveness? Was AA just giving payback for being required to raise $10k in gold?

Lasker probably would still have had good chances of beating Capa before WW1. Capablanca may arguably have been the ultimate natural chess talent ever produced by humanity, but it must be remembered that before WW1, coming from Latin America, he was a relative newbie to international chess. In fact, the commonplace teen-age GMs nowadays have had more international experience than Capa did before WW1.

<James Demery: Capablancas style has been described as being a simple, straightforward style of exchanging down toward an endgame> The more I play over Capablanca's games, the more I realize that his style was not that simple. It seems that in general whenever Capablanca entered a simplifying line, he did so because he had already seen everything until the endgame; and had seen that the resulting endgame was good for him.

Lasker was the first master to play like a super-GM. He knew exactly when it would be beneficial to trade static advantages for dynamic play, increased piece activity, and the initiative. This was seen as sorcery by some, but in fact Lasker was playing at a higher level than the previous masters of his time.

Which is funny, because Kalme in 1975 was trying to argue that the unlimited match system would force players to adapt their styles to be more daring. Usually it had no effect at all, or, in this case, had the opposite effect.

Petrosianic: That's true. Alekhine won the match by playing more like Capa than Capa. His natural enterprising style had failed miserably against Capa in previous encounters.>

Alekhine indeed tried to mix it up with Capablanca repeatedly in tactical games before their match. The result was a massacre.

Capablanca vs Alekhine, 1913

Alekhine vs Capablanca, 1913

Capablanca vs Alekhine, 1914

Alekhine vs Capablanca, 1914

Alekhine vs Capablanca, 1927

While it is true that Capablanca's natural penchant was for solid positional play, at which he was so brilliant that he often managed to steer his games into won endgames while his opponents were unaware of what was really happening before it was too late, Capablanca contrary to popular opinion was the strongest tactical player in his era. His games show him consistently knocking out such strong tacticians as Alekhine and Marshall in complex middlegame melees. This has been often overshadowed by his fundamentally sound positional style, so that most chess pundits have the idea that Capablanca was a solidly boring player.

<A curious phenomenon occurs when I play against Lasker. His qualities as a fighter and his eagerness to play for a win in positions which, strategically speaking, do not entitle any more than a draw to be hoped for, irritate me from the chess point of view, and this increases my efficiency at the board. In such circumstances the fighting spirit is roused in me, and since I am superior to the German in some respects, I manage to beat him at his own game.>

<Poor Capablanca! Thou wert a brilliant technician, but no philosopher. Thou wert not capable of believing that in chess, another style could be victorious than the absolutely correct one. – Max Euwe>

I do not believe that Lasker was ill during the match itself, even if it is possible that he later became ill and quit for health reasons. Lasker played the games of this match magnificently, as though he were in his prime. And he came in with well prepared openings too. Capablanca beat him because Capa was playing just a tad better. All the games that Capablanca won were won not because of a strong opening novelty but only after a hard middlegame and endgame fight. If it were any other opponent, Lasker would have run over him.

Capablanca vs Lasker, 1921 46 moves

Lasker vs Capablanca, 1921 58 moves

Capablanca vs Lasker, 1921 48 moves

Lasker vs Capablanca, 1921 56 moves

These are all over 40 moves and represent struggles at the highest human chessic abilities. To his credit if Lasker was going down, he was going down singing his swan song at the top of his voice.