Your approaches are going to have to be slightly different too, and you're going to want to try some less conventional tactics- like, instead of rolling away? When he tries to shorthop-aerial approach, just WALK back a couple steps to turn around for a tilt.
Basically, my advice is distancing is key through unconventional means (he comes tornado'ing at you? Run! Literally!)
As for egdeguarding/being edgeguarded, try to take advantage of your disjointed hitboxes and the fact that Lucas actually has a pretty good recovery. If you're good at angling your PKT2, than try new, awkward angles that he might not expect.
Also, staying low when you're knocked off will make it harder for him to hit you from the side; he'll have to come from above, and as long as you get your PKT2 out before then he'll have difficulty landing a hit on you.
I suppose it really depends on how HE plays...