Since we're talking bitcoin, then the most sensible way would be
- Take the N last confirmed blocks at time of extraction
- Hash them
- Sign hash with private key
- Treat the signed hash as a huge random integer - extract from it the random number(s) needed for your lottery.
- Anyone can verify that you haven't made it up by verifying the signed hash (using your public key) against the hash of the well-known last N confirmed blocks at time of extraction
- Profit!