Cheapest Method for Lip Augmentation?

It would of course be difficult to alter the lip shape without expending funds for even a filler.
However, it appears the maxilla is long and might benefit from a LeForte I procedure. You may wish to consider consulting with maxillofacial or craniofacial surgeons to see if there is a possibility your insurance might cover the procedure.

This is my philosophy when it comes to these sorts of things. There is a correct way to do things and the incorrect way. To fix a problem, there is a solution and that is the way to go. Anything else will result in expense with no results.

Unfortunately, there is no "cheap" way to augment the lip. You may want to go with fillers temporarily, to see how you like it.  Other more permanent fillers like alloderm or even fat injections may be longer lasting.

There is no easy answer for this question. There are three ways to change the shape of a lip: one is non-surgical, and that is by using a filler of some kind. The second is the placement of a lip implant, and that is surgical. The last is changing the shape of the bony skeleton, which can alter how much teeth you are showing at rest and when smiling, but does not really alter the lip. The third option is covered by insurance in some cases and is done by craniofacial plastic surgeons. The first two options are truly cosmetic and not covered by any insurance.
If you are not a candidate for craniofacial surgery and you cannot afford a filler, then I think you need to accept the shape of your lip as it is. Good luck.