The LSJ thermostat housing is unique in that it has its own two barbs for coolant to and from the oil cooler. The oil cooler is also different from an LNF only in that the barbs are clocked differently to account for different coolant hose routing.
The LSJ thermostat housing also interferes with an F23, at the shifter cable bracket mount bosses, if I recall correctly, so you have to swap to another thermostat housing. The LE5/L61/LAP thermostat housings are all the same, I believe, and the LNF is the same except also drilled and tapped for a coolant line fitting to the turbo. All those motors have the coolant temp sensor in the thermostat housing, whereas the LSJ has it on the head, so the one on the new thermostat housing will need plugged. Most importantly, though, none of those thermostat housings have points to route coolant to and from the oil cooler.
The LNF oil cooler is teed into the coolant return line from the radiator to the thermostat housing and the line from the thermostat housing to the expansion tank. On an LSJ with an F23, to keep the oil cooler, you'll need to swap the thermostat housing to one from an NA Ecotec and plumb new lines and tee splices.