99% chance it's either slugs or snails, especially if they are being more or less completely eaten rather than small holes in the leaves.
As slugs and snails are most active in the middle of the night we don't notice them.
Try putting old orange skins, hollow part down, around the plants, and some bran inside. Also some up-turned pots or a small sheet of plastic. At least you will find some of the pests inside or under these and can destroy them.
Otherwise, put some copper tape around the plants, or slug pellets in an upturned container. Pellets are very wildlife unfriendly though, especially the metaldehyde types which poison the slugs which are then eaten by birds, which in turn are poisoned.
If you are really determined you can set the alarm clock for 3 a.m., get a torch, and go and pick up whatever is eating your lettuce at that time.

thanks bertiefox for your very helpful advise