I actually just got done playing the best Lucas in my area, so here's some stuff that's fresh in my mind:
PK Freeze is super annoying in neutral, but you can crouch underneath it if the Lucas doesn't fire it super low. If you think it's coming, run up and shield to close some distance - then you can wavedash out of it and act from there. If he does hit you with PK freeze, be ready to eat just about anything. Grabs, Fairs, Nairs, even a DACUS if the Lucas is on point.
I've been told I should DI down and away to escape Fair chains, but be careful - if you eat the sweetspot it could result in an early death. The best DI I know for Dthrow is down and behind Lucas, but even then you can get Fair'd. It's better than eating a free Usmash though. AVOID GETTING HIT BY DAIR AT HIGH PERCENTS. It sets up just about the easiest Usmash ever. Dash away and pivot grab for a good punish.
Lucas' Nair, Dair and jab can combine to create insane shield pressure. Jab comes out in one frame, so it will generally beat Up-B OoS - however, the jab itself (and especially jab 2) are definitely unsafe on shield. Once you get an Up-B at low percent, you can Nair > grab > Uthrow > C4 most of the time. Uthrow chain grabs also work - from zero I think you can get four in a row before you should go for the free C4 stick. In general you can combo Lucas just as well as he combos you. Uthrow > Fair can be a nasty early finisher if Lucas DIs offstage, or it can set up a tech chase (and potentially a tranq) otherwise.
Overall, Snake and Lucas both wreck each other hard, but Lucas' PK Freeze and shield pressure gives him the edge in neutral. Maximize your punishes and be smart with your OoS game to combat these advantages.
Also, getting grabbed by Lucas freaking sucks. He can actually get a Dthrow chain grab off of good combo DI, and the active frames on his pivot and dash grabs last for days.