Learn how to control bananas and learn the ways Lucas can utilize them just as much as the Diddy user has learned how to utilize bananas for Diddy. Think of the match as a performance and bananas as a prop that you have to use in the performance. You can't let the prop own you,
you have to own the
prop. You'll be slowed down a lot if you're not in the know as far as banana control. If you don't feel comfortable using bananas, you could always through them offstage and get rid of them every opportunity you get. However, this will put you at a huge disadvantage because the Diddy can utilize his bananas far greater than you can.
If he throws them at you, you can catch them. You don't have to let them bounce off your shield or let them hit you. SH Nair, Fair, Z-Catch, airdodge, and A (grounded) are Lucas's best options for catching a banana when both players are grounded. You can also pick up bananas on the ground with SH Nair, Fair, Airdodge, falling Z-Catch, and rising Z-Catch. Because Lucas doesn't have a glide toss (he does but it's so small and unnoticeable so it's better to say he doesn't), learn how to Jump-Cancelled Item Throw or practice it if you already know it. Input either left or right on the control stick (optional, gives you a slide), Jump and then quickly press A. It's easiest to just slide your thumb from Y to A if you use a GCC and your Y is Jump.
Spend the match feeling out how the Diddy dances around the stage with the bananas. Diddy players have the freedom of major fluidity and stage control, so learn in what ways the Diddy abuses them. It'll be easier to fight a Diddy once you can figure out how and when he uses his bananas. You should try to play slow until you feel comfortable fighting the Diddy while still thinking on your toes. Don't try to stay in a single spot too long or pick up bad habits because Diddy can detect them really quickly with bananas to punish you. You have to feel as confident and comfortable as the Diddy does in this matchup; you can't give him the stage and tell him that he can do whatever he wants with it.
As far as the actual fighting, don't try to punish his dash attack after shielding it. Maybe Jab it if you manage to powershield the dash attack. He usually does it to pick up a banana so you'll be really vulnerable to punishes if you try to punish dash attack. Not to mention his Dash Attack is multihit and is pretty hard to punish just by itself.
Don't try to fish for the kill. Diddy will punish you. Take your time; let the kill come to you. Diddy doesn't exactly have the best kill power, so you'll be sticking around for a decent amount of time per stock as long as your DI is on point. With that being said, there's no reason for
you to try to force kills when he has a hard time killing as well. Just be patient and wait for it. Repedeatly going for the kill will only result in you taking a bunch of damage as well as having a bad habit that Diddy will just dance around. If you hit a Diddy with a SH Banana throw and DI towards him, an Fsmash followup is guaranteed. If Diddy is forced to recover somewhere that's level to the stage, send out a PKT. It'll usually hit him and put him in a really bad spot. If he's offstage somewhere that's higher than the stage, don't bother sending out a PKT. It won't hit him and you'll just get punished. Just try to punish him when he comes down (if it's somewhere near to you). Don't try to chase an evasive Diddy around, more times than not you'll wind up putting
yourself into a bad situation that the Diddy wanted (kinda like vs Wario).
Here are a few ways to use bananas:
http://www.youtube.com/watch?v=M2_K-RBt7qI#t=6m30s
Here's a Lucas player with very good banana control:
http://www.youtube.com/watch?v=UfsH-JRkTh8