Phony Benoni: I just checked the tournament book, and Lasker was indeed White in this game.
The tournament situation coming into the last round:
Lasker, Mason: 5.5
Van Vliet: 4.5
So Lasker was a full point behind Burn, and winning would only enable him to tie for first. Mason had a bye in this round, while Van Vliet had Black against Loman. (They would eventually agree to a short draw, probably after this game was over.)
Lasker had started quickly with three wins in a row before losing to Van Vliet in round 4; he then picked up two more wins, his bye, and a draw.
Burn had started slowly with a draw and bye, but was now on a six-game winning streak.
The tournament had been played at a rapid pace, with seven games in six days.
For those of you who prefer the sordid motive, here are the prizes:
1st 400 f(lorins?)
By winning, Lasker gets 312.5. A draw guarantees him 225. A loss means a maximum of 175, a minimum of 108.3.
Somebody else can figure the exchange rates and mathematical odds. I would incline to <paulalbert>'s view that Lasker had not yet the developed the strength and self-confidence he showed in later years. That's apparent when you look at some of his games and results from this period. Fatigue (he was never a robust young man) and the fact that Burn had all the momentum may also have been factors.
So I would attribute his decision to prudence, but if others want to call it cowardice there is nothing in the situation to contradict them. However, looking at Lasker's play later in life paints a much different picture.