There are crape myrtle trees in the parking space.

Luan tree, the scientific name is full-leaf Luan tree.

I have seen a lot of oily things fall under trees, but mainly in the season when there are fruits, so I thought it was the oil oozing from the seeds in the fruits. There is no fruit on your tree. It may really be secreted by some insect on the tree, as your friend said.