This is actually a pretty interesting idea. The prize itself should be limited to the key and not the cash for entry too. There should be a threshold of players met allowing the lottery to go through for that day though, otherwise we'd end up with only a few participants some days. Like a 10 player requirement otherwise it waits until that requirement is met. It could also be that depending on how many players participate, a certain amount of keys is awarded. This would have to be weighted based on how expensive the entry price is.
Example:
10 players = 1 key
20 players = 2 keys
30 players = 3 keys etc.
An identifier above the lottery NPCs name for how many players have entered would be a nice UI feature.
ofc, if no one cares about any of what I just said, I support the original idea as is too.