Can a lisp be a dental problem instead of a tongue placement problem?

Yes, but not always: The tongue is the only muscle with an origin but no insertion. It has full freedom to make infinite movement. The only thing restricting it is the frenulum, causing it to be "tongue-tied" in some people. The tip simply cannot push out and past the lips. In severe cases, it can't touch the upper front teeth to make sounds. If they are missing or in the wrong position, lisping can happen.

Yes: If teeth are misaligned, it can cause a lisp.

Yes, kind of: The dental aspect would be related to the tongue placement. If the teeth cannot properly approximate themselves for certain sounds, the tongue often steps in and tries to help. See a Prosthodontist to evaluate the tooth position for proper speech and a speech therapist/pathologist for further assessment and treatment. Good Luck.

Of course: The lisping may be caused by number of dental issues like gaps between the teeth, malocclusion and overbites. The good news is these types of dental issues can be solved by standard orthodontic treatment.