Yes, it is normal to have speech differences when teeth are added (crowns, bridges, dentures) or removed, as is your case. As long as you don't have any other symptoms such as a stroke or palsy or something else medically related I think it is the tooth. Usually a back tooth won't cause a lisp but every is different. I'd get an implant in that spot if you can. If not, get a bridge.
Your descriptions suggest that your tongue movement may be impaired due to nerve injury. Going back to your dentist to have a posy op exam is advised.