Can rabbits have cucumbers? I didn't know about that!
Candice, fruit should be given as treats, so just give tiny pieces every once in a while (I give it about once or 2x a day, then I spend some time without giving any 'cause my bunny is a little fat). Banana, mango, peaches, fresh plums, strawberries (and strawberry tops) are very appreciated by bunnies. My MILU also likes oranges, but I don't know how many rabbits would like it, since I myself am not a big fan of them.
Yes, lettuce shouldn't be given although I know people who give romaine lettuce to their bunnies. I try to stay away from trouble, so I only give what I know is safe.
Good veggies are carrot tops, broccoli leaves (or florets), cabbage....