"Do I assume that if the cages won't turn easily, it needs to be lubed?"

YES

"I'm also assuming that I need to remove it from the car in order to get the ATF in the right places."

Once you can see the cages, one clip [towards front of car - tip: insert pointed end of long nail punch {whatever} and push down - clip will easily pop open.] releases tensioned bracket, disconnect 2 wires and and motor w cages lifts straight up and out. Hold motor w cages vertically and use tranny dip stick to dribble ATF onto mating surface of both sides. Spin & smile!

"Are the filters side by side?"

YES

"I guess I should order 2 new filters since I know they haven't been changed in at least 4 years."

2 pieces come as one set in a box. "cabin filter" $21 autopartsguru and others

Bob