I have a soft lump near the corner of my mouth.

A soft lump can be a lump of fat or a small cyst.  Without knowing more about your procedure or seeing your pictures it is difficult to answer what may be going on.  An in-person examination by your plastic surgeon is probably in order.

Sounds like a buccal fat pad protruding. You need to see a doctor who knows how to remove this from inside the mouth which can be done in the office under local anesthesia. If this does not work then the face lift flap needs to be opened up and the weakness of the fascia closed with a suture. Not all doctors you see may be willing to do this, an experienced doctor with maxillofacial training may be best.

The lump could be several things including buccal fat and a tortuous artery. Also if any filler was used it could be from that. Each would have a different treatment so it's important to find out for sure. You need a good exam. Good luck.