is LP gained determined prior to entering the game?

It sort of is. The LP gain is a factor of your current MMR compared to what is the expected MMR for your rank. If your MMR is higher than expected for your ranking, you'll gain more LP. If it's lower than expected, you gain less LP.

Since all those values are known by the system before the game starts, I guess you could say the LP gain for that game would already be known beforehand.

Yes. Your performance in the match doesn't affect the outcome, your gain depends on the perceived difficulty of the match by comparing your MMR to the opponent's.