I see two main options, since your system is at 12VDC volts, and your mains at 120VAC, as you've noted it makes sense to use one or the other for the lights.
120VAC:
The bulbs are much cheaper and readily available most everywhere (at least where I am at)
Switching between the mains and the inverter could be as simple as a double pull, double throw relay, (switch both the neutral and the 'hot' line as the grounding schemes are likely different unless you want to see some of Ghurd's magic smoke) although the building codes may not allow for that in your area. It probably wouldn't be that hard to rig a simple circuit to throw the relay when the battery voltage is above a minimum level. I've used this scheme before, the lights flicker when it switches back and forth from batteries to grid.
An alternative would be to build a circuit to switch on and off the inverter depending on the battery voltage.
12VDC:
Although the bulbs are more expensive, you don't have losses from the inverter.
Again, you can probably rig a simple relay circuit to turn on the grid-tied charger when the batteries reach a certain discharge voltage.
I have a pile of solid state relays that I purchased surplus, so I would probably use one of those on the 'hot' leg of the charger supply and then use a common op-amp comparitor circuit with a resistance voltage divider tied to the battery voltage on one leg of the op amp and a reference voltage set by a zener and a resistor on the other leg to switch on the relay. You will also have to add a feedback voltage from the output of the op amp to the voltage divider or reference to provide some hysterisis. For the 110AC version, I would use the comparator circuit to turn on a transistor that would power the coil of a traditional DPDT relay rated for more amps than needed, and protected by a fuse. In either case, the lights would simply operate from the switch as normal (dc switch if 12VDC), with the user oblivious as to how it was powered without checking.
Anyway, just kicking around some ideas, Rich