Any type of liposuction can be done under local anesthesia as long as the amount of the local anesthesia given doesn't exceed the amount toxic to the body. As long as the areas to be worked on are numb then the procedure can be done. The possible problem that can occur is if too large an area to be covered by the appropriate dose of local anesthesia is chosen to be worked on and then the patient may have discomfort.
Any type of liposuction can be done using local anesthesia. For larger areas iv sedation keeps the patient more comfortable and for large volume liposuction the patient is more comfortable under general anesthesia and it is safer because it eliminates concerns about lidocaine toxicity.