Do slightly elevated liver enzymes pose a problem under local anesthetia ?

The question is not whether liposuction under local anesthesia is safe in the setting of elevated liver enzymes but rather why are the enzymes elevated. There are a number of different reasons for an elevation (some more concerning than others). I would recommend you seek a proper work up with an internist or gastroenterologist prior to contemplating elective surgery.

Dear somers3219, Although local anesthesia poses less of a risk than general anesthesia, it is still important that you determine the cause of the elevated enzymes. I would discuss with your operating surgeon, who may request that you have more tests completed prior to operating on you. Good luck!

The answer depends upon why the enzymes elevated in the first place. If you have a stable condition there should be no problem. If this is a sign of hepatic deterioration that's quite another matter.