Puzzling electrical problem with 9 wires in junction box
Assuming that box is wired correctly and to code, it looks like this would be true:  

The lower right is the cable from the service (always energized).  Its black is always-hot and its white is always-neutral.  (all the neutrals are always-neutral; this setup properly switches the hot.) 

The upper cable is the switch loop.  The black wire is always-hot.  Switched-hot comes back on the white wire, and that wire should be wrapped with some electrical tape to designate it as a hot.   Historically that marking wasn't mandatory if the application was obvious; do you think it is obvious? 

The black wire to the light fixture is switched-hot.   The white wire to the lamp is neutral.  

The lower left is the cable to the other light fixture. It is the same: black is switched-hot, white is neutral. 

Equipment safety ground is all tied together, of course.