The short answer
Leafy lettuces yes — but iceberg only sparingly.
Why
Dark, leafy lettuces like romaine and red-leaf are safe, hydrating and fine to offer often. Iceberg lettuce isn't toxic, but it's almost all water with little nutrition, and too much can cause loose droppings.
How to feed it
Wash and offer romaine or leaf lettuce; use iceberg only as an occasional watery snack.
How much & how often
Leafy types can be frequent; iceberg only now and then.