FOLLY: That's about N3,333 per person. I don't think you can get a sit down lunch in Lekki/VI for that price. Starting price for mains at most restaurants is about N3000 - N3500, and that's not counting starters or drinks. If you're flexible with your budget and would like to go up to N4000 - N4500 per person, I'd recommend Crust & Cream. However, if you're firm on the budget I don't see any other way but BBQ & Cravings.
NOSA: I second that BBQ & Cravings motion
FOLLY: Deli's has a nice pesto chicken sandwich. It's not fried but I like it.
NOSA: Don't think any place does it. Smokey Bones has BBQ Chicken sandwich with coleslaw in it, which isn't what you asked for but it's close.
NOSA: Try NOK by Alara. It's adventurous enough for her, but safe enough for you. At your budget, I'd skip the alcohol though.
FOLLY: Crust & Cream cause they have a bakery.