I would classify a lisp as a speech sound/articulation disorder and it could have a neurological basis as the motor planning for those sounds is not automatic.
Yes, a lisp can be treated with therapy as with most communication disorders (any hearing, speech and/or language disorders that are developmental or acquired that may impact receptive and/ or expressive language as well as spoken and/or written language in one or more of the following semantics, morphology, syntax, phonology, and pragmatics). People may overcome a communication disorder in language or they may learn how to compensate for the disorder. And a lisp could impact a child's willingness to speak for fear of teasing therefore impacting the quality of life and qualifies as impairment by the World Health Organization.
Also as in any articulation disorder it can impact how the child spells words. He/she may spell words as they are produced. Suspected speech and/or language disorders should be evaluated by a certified Speech Language Pathologist (SLP) and hearing disorders should be referred to a certified audiologist.