Are there adverse effects to taking amoxicillin for respiratory infection while on lamictal, have epilepsy and nafld (genetic etiology)?

No adverse effects. Amoxicillin is primarily excreted in the urine, mostly as unchanged drug; only 10% of Amoxicillin is metabolized by the liver, and there isn't felt to be any need to adjust Amoxicillin for hepatic impairment (thus, no worry about nafld). There is no drug interaction with lamictal. You're in the clear!