All three are slightly unnatural, as they suggest that we'd like just one vegetable/salad item for lunch. We are more likely to say, "I'd like some X with my lunch".
1. Aubergine (BrE)/eggplant (AmE) is normally non-count, because we do not normally see the whole vegetable on our plate.
2. We could express our wish for a tomato (probably large), some tomatoes (probably small), tomato/some tomato (probably sliced). It depends on how we visualise the food at the moment of speaking.
3. Similarly, we might want a potato (probably baked), some potatoes (probably boiled), potato/some potato (probably mashed), chips/some chips (BrE), fries/some fries (Ame E)