I would base it off of something blockchain related and out of your control... Just an example here to give more ideas:
Since you list the transactions on your site, you can base something off the blockchain. So let's say the 10th ticket transaction of your 10/10 lotto is in block 318117, the winner could be determined in the next unmined block 318118. An example is maybe the last integer in the hash of the block, so for 318118 the hash was 00000000000000001f1c023df24bece678182e21a73f493d8316d62ee78895ae, so the winner would be ticket #5.
Or something based of anything in the blockchain that is not predictable but fits your pool of tickets to pick a winner, the mod of transactions in the block, etc.
-C
Alright, that seems like a good idea...
But ... let say i do that. I would then have to explain that on the website. Most won't understand that system... but also, those who will, will be able to decide if it's worth it to play or not. Like : wait to get 9 tickets in, see if it is worth it to buy the last ticket not... No ?
You don't have to explain it to people that don't understand. To them you say "picked a winner at random"