It will not be 25 BTC fixed, it will vary depending on the fees. And the lottery is not ment to prevent sybil attacks, since it doesnt replace mining. And the selection of the random addresses can be done using the blockhash fairly simple. If you want I can give you a technical implementation of it, but it goes out of the scope of the topic I guess.
The miners will just game this by filling blocks with txs back to themselves with high fees. If the tx in the block are 99.9% belonging to the miner then they have a 99.9% chance of winning the lottery. If anything you just created a disincentive for a miner to ever include a legit tx unless it has an extremely high fee (as it would serve no purpose except to lower the miners chance of winning). Since miners recover the fees paid on their own spam, there is no cost to the miner and they can make the block reward as large as they want. This will put upward pressure of fees such that blocks will be mostly filled with miner spam and crowd out legitimate tx volume. It is a minor issue but it would also greater incentivise selfish mining as optimally a miner would want to be 1 block ahead of the network to ensure it doesn't lose fees paid to itself in the event of losing a race.