Your fsmash is quick and strong, you should be able to kill in the low hundreds with it, if you can predict. It has quick enough start up to make it viable for punishing most slower attacks.
Ftilt is very easy to hit with, and if you find yourself getting up to 170 or so, it should be able to kill fairly reliably.
Dsmash has multiple hits, which makes it great as an anti-dodge attack. If they spot dodge, it will almost definitely hit with one of the last hits. The same with a roll, if they are still within range. There is a brief moment of time when you are unable to do anything after landing, and if you are already doing a downsmash when they land, even if they airdodge as they are going down and shield the first chance they can, it will hit.
I would avoid the up smash, its just too slow and unwieldy to use except in weird situations.
Your throws are good, although like someone else said, punishable. Down throw kills vertically before upthrow will, but if you are near an edge, backthrow will probably kill before dthrow will.
That's a very brief guide to lucas's kill moves, but there are definitely better guides and more knowledgeable people on the lucas boards.