Poor baby!
Not lactose intolerance at this age (would be from birth or school-age-ish), though 2ndary LI is possible as a result of the diarohea (I can never spell that word). If so, that would sort itself out once his tummy is better.
Is your topup formula dairy based? If so, and this is a new problem, then unliekly to be dairy allergy I guess. If it started with the introduction of new foods, then it could well be some other allergy - which has had knockon effects lasting this long... maybe?
Viruses can certainly have this effect, also. Maybe get the sample done and see what that can tell you?