Just speaking from my own experience... I ended up taking care of a little 4 week old doe that had been weaned too early and improperly, by being fed only lettuce and bits of carrot by the original owners. When I started caring for the baby she was quite underweight and skinny. She wouldn't touch pellets and hay, and the fresh forage I was able to give her (and that she would also eat), upset her stomach so I couldn't continue it. I even tried putting her on milk replacer and fresh goats milk, but she wouldn't take it. I had really tried everything, but the only thing she would eat that didn't upset her stomach, was lettuce. So that's what I reluctantly fed her. And she ate a ton of it. She was only about 4 oz. and ate a whole head of green leaf lettuce in a day. She did pee a lot because of all the water content, but she also thrived, put on weight, and grew. Poos where a bit dark and elongated, but otherwise normal. So I didn't feel she was missing out on anything nutritionally during this temporary blip in her diet. Gradually over the next two weeks she started sampling other foods and eventually she was eating pellets, hay, and herbs, and I was able to mostly wean her off of the lettuce. It took a while to get her off of lettuce because she also didn't know how to drink water, so I used it to supplement her fluid needs until she did figure it out. Now she just gets a small amount as a treat.
I do still feed some dark leafy lettuce to my rabbits just as a treat because they all love it, and I have never encountered any ill effects from feeding it to them. I don't know if iceberg is safe though, as I've never dared feeding it due to the warnings about feeding it and the firsthand accounts that I've read of others feeding it and their rabbits getting diarrhea(but this could be down to inexperienced owners feeding too much, too quickly).
I would imagine that like celery, lettuce may also be a beneficial veg to feed for bladder sludge issues, due to it's high water content. But this is just conjecture on my part.