I don't see how Lucas can use your bananas against you any easier than your average character. He doesn't have a reflect move... in fact is absorber is completely useless vs. Diddy. I would think it would be quite difficult to face Lucas without using your bananas, as his PK Fire and other abilities make it very difficult to approach.
If he is using your bananas against you, not using them at all is probably not the answer. Because that gives him a really big advantage. Instead, use them more sparingly and carefully, and try to find new ways to use them, and surprise your opponent with them.
Remember that just the act of using bananas won't help you. At all. The bananas create openings. Always follow up bananas with assault, or it will be very easy for your opponent to use them against you.
And if your opponent goes off the stage... FOLLOW HIM. Every time. Diddy has a great recovery, and you should use that to your advantage. Often just the act of following him off the stage can cause problems for your opponent, as it pressures him to be extra careful, or to do something he wouldn't normally. If you're following him off the stage from the start, it will probably be much easier to get a Diddy Hump off. Predicting your opponent is the key to edge-guarding, so try to figure out how he will react.