All it does it change the random, which leads to a different winner.
The assumption is that the miner would be changing the winner to themselves or someone who is willing to split the prize with them. But as above, the chance of them finding a block which also picks the "right" winner from 100 or more tickets is very small indeed.
In case of collusion with miners to cheat the lottery, I would assume the host is in on it. So the miners will know the content of the hidden hash, and can use that to alter the outcome.
So you get the host to commit to a block number without revealing it, such as via a hash as I suggested above. You also get every participant to commit to an offset number, also without revealing it, say between -500 and +100. Assuming the number of participants is
n, then the host waits until 100*
n blocks beyond the block number they chose (just in case every participant chose +100 as their offset number), and then reveals the block number. All the participants also reveal their offset number, everything is summed, and that is the block number you use to pick the winner. Provided at least one participant is honest, then the block number cannot be predicted. And if every participant is in on the scam, then what's the point in the first place?
But again, this is all needlessly complex and would only even be worth thinking about if the competition in question had a prize worth millions or even tens of millions of dollars.