You make great use of Lucas's aerial and tilt attacks. I think you overuse PK Fire. However, when you do use it, you do the right thing in hopping, first. Try shooting another right when you hit the ground. You should find that the one you fire on the ground comes out much faster, because landing cancels the lag on the aerial PK Fire. I also think you should make more use of his powerful smash attacks, especially his down smash. It has good range, duration and killing power. Also look for opportunities to land grabs, since throws can set up for combos or smash attacks such as the up smash. PKT2 is a great way to gain damage on an opponent, so you could try using it more, and I didn't see you use PK Freeze even once. In some cases, especially at higher damages, chasing opponents over the edge yourself might work better than chasing with PK Thunder.
In short, you've got a good foundation but you should try harder to use his full range of moves.
