Did it make sense for Lasker to play the Exchange variation of the Ruy Lopez in 1914? In 1914, world champion Emanuel Lasker was trailing future world champion J.R. Capablanca in a tournament, meaning that he needed to win, not just draw, against Capablanca.

He played the exchange variation of the Ruy Lopez, trading his best attacking pieces, his queen and light squared bishop, early in this classic game.
For these reasons, the variation was considered "drawish." Except that Lasker won.

Here's some background that may explain why:


Lasker was the best endgame player in the world. Capablanca was inferior (at the time) in this regard. (Both of these opinions are Capablanca's.)
Capablanca was already a ferocious middle game player (and seen as such).
At the time, Lasker was 46 years old and Capablanca was 26. Lasker was more "mature." 


In "Chess Fundamentals," Capablanca noted that immediately after the queen exchange, "The reader should note that if all the pieces were exchanged, White would be practically a pawn ahead and therefore have a won game." In fact, Capablanca was "rattled" by the prospect of a lost endgame and therefore misplayed what passed for a middle game.

Even though it was regarded as "unconventional," did Lasker's strategy make sense from the point of view of his endgame advantage?
It made perfect sense.

He was very familiar with the opening:


  Lasker played hundreds of practice games with the Exchange Variation of the Ruy Lopez and discovered what he thought was every mistake White or Black could make.


Source: #247: 300 Wisest Things Said about Chess: With 300 Annotated Positions

Lasker was well known to adapt his playing style to the opponent's psychology.


  Lasker was considered to have a "psychological" method of play in which he considered the subjective qualities of his opponent, in addition to the objective requirements of his position on the board. Richard Réti published a lengthy analysis of Lasker's play in which he concluded that Lasker deliberately played inferior moves that he knew would make his opponent uncomfortable.


Source: wikipedia

Your research has shown that the opening took Capablanca out of his stride and scored the full point, so yes it made perfect sense.