They did not meet at the 1939 Olympiad because Capablanca had said that he would not play against Alekhine.

From Capablanca's article in <Critica>:

<Last night’s match between France and Cuba was drawn two-all. I should like to explain my absence, which was due to purely personal reasons.

Neither France nor Cuba was a leading contender in this competition, which meant that from that point of view there was no special significance in whether or not I played. There was only the question of the spectacle itself, which of course could not influence the course of the tournament.

Once more it is necessary to emphasize that the event being held at the Politeama is a tournament for teams, not individuals. A week ago I notified the Argentine Chess Federation that I did not intend to play against Alekhine, and I explained my reasons for this decision.

I made this announcement to the Federation so that my intentions were known in advance, and to prevent disappointment on the part of the public. My not playing yesterday was thus not an act of discourtesy to the Federation, nor a lack of consideration for the Buenos Aires public.

A normal retreat would do, but is unlikely to achieve anything right now - although White would still have an advantage, it wouldn't be in keeping with the fact that this is a Tuesday puzzle either.

No forcing Queen moves suggest themselves; neither Qh6+ nor Qxg6+ nor Qxf6+ appears to do anything but drop the Queen. So it's not a retreat or an immediate sac; what else can we do? Obviously a check as fxg5 can't be allowed, and there's only two of those: Ne8+ and Nf5+. Ne8+ doesn't lead to anything either, therefore -

25 Nf5+

After which Black's King goes into the corner and now both Queen AND Knight are attacked. No Knight move suggests itself that doesn't just let the Queen be captured with no followup; a Queen's retreat drops the Knight, and while at first we might see that this opens the g-file, there is no opportunity to create a battery, for after 26 Qg4 gxf5 the Queen is attacked again, while 26 Qg3 blocks the square by which the Rook can enter the file.

However, this battery motif does note something - considering the position after, say, 26 Qg4 gxf5 27 Rg3: what if Black *couldn't* capture the Queen? Mate would be threatened at g7, that's what, and it's also not preventable, because Black can't safely occupy f7: 27 ... Rxf7 28 Bxf7 and (again, assuming PxQ wasn't an option) mate is forced.

Therefore, *g7 is vulnerable*. And as we need a forcing move with two pieces under attack, what about 26 Qxg6? Again we're threatening mate at g7, and again Black can't simply protect the square because BxR destroys all hopes. Again, the Queen can be taken: and, indeed, in light of this it *must* be taken. So -

26 Qxg6 hxg6

And during that 9 year lay-off, Lasker was still giving exhibitions, so it was not that he had retired fully.

25. Nf6+ is forcing, and the follow has to be
25. ... Kh8

and if now

26. Qxg6! the h pawn cannot capture because of
27. Rh3+ and mates in a move or two. So now how does Black stop mate on g7?

26. ... Rf7
27. Bxf7

I don't see a move beside Rf7 that stops mate by the Queen on g7.

So 25. Nf6+ followed by 26. Qxg6 it is.

And, just to make sure I've exhausted the defense:

<In spring 1933 Adolf Hitler started a campaign of discrimination and intimidation against Jews, depriving them of their property and citizenship. Lasker and his wife Martha, who were both Jewish, were forced to leave Germany in the same year. After a short stay in England, in 1935 they were invited to live in the USSR by Nikolai Krylenko, the Commissar of Justice who was responsible for the Moscow show trials and, in his other capacity as Sports Minister, was an enthusiastic supporter of chess. In the USSR, Lasker renounced his German citizenship and received Soviet citizenship.[90] He took permanent residence in Moscow, and was given a post at Moscow's Institute for Mathematics[65] and a post of trainer of the USSR national team. Lasker returned to competitive chess to make some money, finishing fifth in Zürich 1934 and third in Moscow 1935 (undefeated, ½ point behind Mikhail Botvinnik and Salo Flohr; ahead of Capablanca, Rudolf Spielmann and several Soviet masters), sixth in Moscow 1936 and seventh equal in Nottingham 1936.[92] His performance in Moscow 1935 at age 66 was hailed as "a biological miracle."

Joseph Stalin's Great Purge started at about the same time the Laskers arrived in the USSR. In August 1937, Martha and Emanuel Lasker decided to leave the Soviet Union, and they moved, via the Netherlands, to the United States (first Chicago, next New York) in October 1937.>

After castling and intermediate move 14.Nf5 to make black Q retreat before recapture, 15.N3xd4! was strong, if 15.Qxd4 then 15...Nb6 to exchange Qs equalizes immediately. Now after 15...Ne5 to make N more active with 16.Bb3 also strong, 16...Bxf5 solves basic problem of black LSB in QGD by exchanging it away. After recapture 17.Nxf5 it would be mistake to exchange Qs via 17...Qxd1 18.Rfd1 because white B on b3 dominates position for advantage. Here was critical position, N on f5 was dangerous piece and correct move was 17...g6! for likely draw, this was tested later in Euwe vs Flohr, 1936 see Alekhine's annotations there.