True - I did not only give him lettuce, but, leafy greens and veggies. The shredded carrots and avacado were his favorites. Sometimes he liked tomato, but not too often. I tried to give him nutrition, not just greens. I wish I had known then about the powder supplement.
What other vegetables would be good for them? What about fruits?
I think just about anything they want. If I have it, they have it. I often catch them eyeballing me if I'm eating something they want to try, so I give them some. The female really loves my pasta sauce. I put some on the tip of my finger and she goes to town. I usually do give them a separate little plate of cut up fresh fruit along with their plate of veggies and their water dish is full of chopped greens. Try cutting a grape into 20 separate pieces. Their mouths are so tiny, they'd wrestle with a whole grape and never get any.

Tomatoes aren't really recommended for iguanas. I have a list of the best and worst veggies and fruits for iguanas, according to the Calcium/Phosphorus/Magnesium ratios, around here somewhere. My vet gave it to me. She is a reptile specialist. If I can find it I'll just copy it in a post for you.
Today, the girl was doing some kind of little jig in the middle of the floor. I was watching her. She was running in circles and kicking her back legs out sideways. I watched for a minute or two then decided to pick her up and see what's shakin. Hahahaha. I held her up so I could see her underside. Half her body was shedding. She looked like an old man peeling off his thermal underware. Hahahahaha. I helped her along by doing some peeling. Right down her belly to the tips of both back legs. She was fine after that. When they shed they get a bit cranky, even the male does. I am guessing they MUST itch something awful. Frequent soaks and misting facilitate the sheds. In the wild they'd be rubbing up against rocks and trees to get the dead skin off. All the branches I have for them have been stripped of the bark for cleanliness reasons.
Beardies seem to shed in much larger sections than iguanas do. Their sheds are more of patches here and there.