I installed a GFCI in the upstairs bathroom, outlet works fine and the 'load' portion powers all the other light circuits okay with one exception. The GFCI pops every time I turn on the hallway lights (3-way switch). However, same wall box shares stair light circuit, also with 3-way switch and it doesn't cause any problem with the GFCI.

It could be a problem with the lights or a switch or a shared neutral on the circuit.

If the light circuit didn't throw a breaker before, connect the hot lead to the light wires, probably like before and pigtail a lead to the GFCI. That way, the bath is protected on its own. Many electricians will not put lights on a load side because if the GFCI trips you will lose lights and have to wander around in the dark to reset the GFCI.

Everything on the Load side of the GFI has to be equal.
Hot and neutral on all loads must be on the Line OR Load side.