i play against a very good Lucas, so i think i can help.
shield is your friend. shield graabbing more importantly. since there is a reasonable bit of lag after a PK fire, shield>dashA>Up Smash works great. Lucas' airs (some anyway) have almost zero landing lag, so he can land and go straight into a neutral A combo, so prepare to roll backwards or shield when he lands.
something a lot of people forget is that Falco's down B can still reflect projectiles including a PK fire.
Lucas' recovery isnt as gimpable as Ness' but (if your ninja enough) you can shoot his thunder, or reflect it (Down B). his thunder is so slow, once it's off, he cant catch up with it.
dont try to roll past lucas while he does his Fsmash, Dsmash or Upsmash, they hit from behind.
SHDL to counter a PK fire is very effective.
chain grab, spike, all the basics.
look out for lucas' air moves. they have more range and sweetspots than you.
basically keep him away until he ****s up enough to punish him.
