When you dismiss the fact that people in any time period are suicidal (the book mentions that some Lives come from asylums), there are still a couple of reasons given or implied within the text. It is explicitly stated that
members of the Despondent sect could be persuaded to become Lives,
either for free or for a donation to their cause.
There is an implication earlier in that paragraph that the Lives get some kind of share of any winnings, and might even be allowed out of prison sentences in order to participate:
...Players, like Kraiklyn, had the sweepings of prisons and asylums, and a few paid depressives who had willed their share of any proceeds to someone else.
Lastly, there are:
the moties: victims of the game's emotional fall-out; mind-junkies who only exist to lap at the crumbs of ecstasy and anguish falling from the lips of their heroes, the Players of the Game...
The closer you are to the Game, the more pronounced the effect of the emotional feedback you feel; it's not difficult to imagine from the portrayal of "moties" that some of them might have found the only way they could continue to get the "fix" was to get right into the game itself, as a Life.