Lichess needs money itself. It survives off donations.
The evidence points that it is pretty far from being able to sponsor chess players and let them make a living from doing what they love, like a commercial platform could do.
If you read my comment carefully you'll find I didn't say lichess themselves could sponsor prize funds. I explicitly said they'd have to source the funds from other sponsors.
The problem is that companies like chess.com and chess24 tend to sponsor these things, and they're in direct competition with lichess.