I don't think you would be able to forge your own ticket. For example, the lottery tickets could be "purchased" by sending some amount of BTC to a special/none

I don't think you would be able to forge your own ticket. For example, the lottery tickets could be "purchased" by sending some amount of BTC to a special/nonexistent address, and these transactions would be required to be present in the block being validated for the block to be considered valid. Admittedly I haven't thought about all the details but it would surprise me if there wasn't an obvious alternative to the proof-of-waste system currently in place.