I would not recommend doing a Tummy tuck or BBL under local. The amount of local required for those procedure might be close to levels of lidocaine toxicity and not be safe. However liposuction can be performed under local with careful calculation of medications used. Please discuss with your plastic surgeon.Good luck!!
General anesthesia is a safe and comfortable option for tummy tuck, and I would not even think of doing it under local. Given the amount of tissue that would have to be numbed with local, that would likely be the riskier approach.