Can I have 360 liposuction under local anesthesia after a pulmonary embolism?

I would avoid doing liposuction or any elective cosmetic surgery after a PE regardless of whether it is under local anesthesia or a general anesthetic and regardless of whether you are cleared or not. 

you would need to be medically cleared but yes this is possible depending the area covered and type of procedure (agressive nature or not versus fat grafting etc)
You need a formal evaluation by an expert in body shaping and contouring to determine what is best.  Traditional liposuction awake and smart liposuction are old methods and do very poorly for tightening skin or significant skin tightening or contouring.  Small problem areas can be improved slightly by these methods.  The best in body contouring not only removes fat with energy devices like VASER ultrasound but also internally heat the skin with radio-frequency devices such as J PLASMA/RENUVION, InMode BodyTite, ThermiRF to heat the under surface of the skin and tighten it at the same time as fat removal. These combinations are called 4D HIDEF VASER contouring and can only be done by a well . trained body contouring specialist. At the same time fat should be harvested, PRP and stem cells added and injected into muscles or indentations/cellulite to get body shaping and contouring.  This is known as a Brazilian butt lift when you inject the fat to the buttock for contouring and lifting, but fat can also be used in areas such as the chest/breast, arms/shoulders, calves and face.  Cellulite should also be treated with cellfina, sculptra, subcision and/or fillers such as bellafill, renuva synthetic fat, or sculptra.  If skin is very loose before surgery then it will need to be removed such as lower abdominal skin (tummy tuck/abdominoplasty), breast skin (breast lift), arm skin (brachioplasty).  Overall you need a full assessment, but simple liposuction alone will not tighten skin and needs a combination of various methods -- fat removal, skin tightening, defining, fat grafting, skin removal -- to get the best in body contouring and body sculpting.  Dr. Emer.

It is possible to do it but it would require solid preparation, including clearance by your pulmologyst. Monitored anesthesia by an anesthesiologyst is recommended. Carefully choose your surgeon and facility since risks may be unpredictable. Good luck.