The first lesson to be learned from this war is that it is very difficult to subdue a nationalist force, even one that is much less well-equipped. This is true even in a situation like the Philippines where there was no outside power helping the “rebels” and some major portions of the population supported the US.
A second lesson is that such wars lead to atrocities. This is true of both sides of the conflict. A final lesson has to do with the aftermath of the war. It is very difficult to impose a system of liberal democracy on a country that has no history of such a system.
Of course, these lessons are the ones that we see from our perspective today. That perspective may be altered by things like the Vietnam War that have happened since we fought in the Philippines.