I am lottery solo mining with an old asic miner on bitcoin-0.19.1 as I believe this is the last version that allows solo mining. Am I still viably solo mining (albeit with extremely little chance to win, sure) even though I am on an older bitcoin version?
No major upgrades since the 19.1 version you have, I don't think using an older Bitcoin core version will affect your mining operations, although the other obvious things such as sustained and reliable connectivity and availability might do, you could use a solo pool and pay a small fee,
cksolo has a 2% fee, Viabtc charges 1%, a few other pools offer the same service, which is a lot safer than mining to your own node.