The tongue poking through can also push teeth out of alignment, which just makes the gap more pronounced so the tongue goes through, which pushes the teeth …
Its as much an orthodontic challenge to make sure the teeth are closing properly as getting a speech therapist to train your friend to place their tongue properly. Orthodontists can add ‘spikes’ to some of their braces to discourage the tongue from resting in certain positions.
According to the Wikipedia article on “Lisp” there are several different kinds, including a “strident lisp” which is sometimes called a “whistling s”. It’s described:
A strident lisp results in a high frequency whistle or hissing sound caused by stream passing between the tongue and the hard surface
I have this. I’m putting my tongue nearly on the roof of my mouth behind (but not very close to) my front teeth. I don’t hear it so much when I speak but when I hear recordings of myself I easily notice it.
Whistling sounds depend a lot on the exact geometry the air is rushing through, I think. Perhaps this particular lisp depends on details of the shape of the forward roof of the mouth. Nobody has ever told me there’s anything out of the ordinary about my teeth or mouth.