Summary of Q: If everything a person does is motivated by some purpose, how can anything truly be lishmo? Surely every motive can be traced back to personal gratification? (Based on the Rambam’s definition of ???? ???? ???? ???? ???)
A: Clearly, the solution will have to divide various motives into two categories, and find an underlying factor that will be a defining point whether a motive is considered ulterior or otherwise.
Here’s an attempt: Every action can be split into two categories – Instinctive and Deliberate. An animal only acts instinctively, whereas humans have the ability to use intellect to make conscious decisions. But a humans actions can be split further. Even the conscious decisions can be split – either a response to an urge or external drive, rendering it more of a reaction than an action, or – more rare – a conscious deliberate decision to do something for another reason.
For example, on Shabbos in the winter, after a long Shabbos-Rosh-Chodesh-Chanuka-Bar-Mitzvah in Shul, you come home famished, and tuck into your wife’s steaming cholent. This action falls into the first category – although you decided to eat the food, it was a response to the hunger pangs assaulting you.
An hour and a half later, however, it is almost shkiyah, and you have to wash again for Shaleshudos. You cannot eat another morsel, yet you force a kzayis down. This is not motivated by any selfish reasons; you are doing it purely because Hashem said to eat.
Perhaps that is ???? ???? ???? ???? ??? – If the motive is because you feel it is the right thing to do rather than for personal gratification, you have hit lishmo.
(Although I understand that this does not answer PAAs question entirely, it could be pshat in the Rambam. PAA agreed that you can redefine lishmo to answer the question, granted that it works in the Rambams loshon.)