Hmmm, how to answer. First, in full disclosure, I'll declare my personal bias: I would not like to see a bunch of gringos flying around on resident fares and a public forum is not a good place for declarations of doing this. Given my bias, three points:
On another board there is someone who claims to do successfully as you suggested. However, he has a Peruvian wife who checks luggage etc. while he stays in the background.
There is risk doing this. Probably less if all goes well, very high risk when IRROPS etc happen. Probably less in Lima and higher risk at the regional airports. If you do it infrequently, less risk; if you do it a lot, then a situation will likely arise. How the situation is resolved will depend on how nimble you are on your feet.
Why take the risk? LAN is ripping off non-residents, why support LAN at all? There are great less expensive alternatives: Star Peru, Peruvian. (not TACA, they are copying LAN).
Note: The recent Peruvian situation most agree was more political than real and was resolved quickly. Indeed, Peruvian is now under more scrutiny than LAN and is crossing all the “t”s, so a good time to fly them.