How much power is required to run LEDs?
To figure out how much running time you will get from any Solar/LED system, you need to quantify two numbers:

The watt-hours of your battery bank. You said you have eight 12V batteries in your current setup, now you need the capacities (in amp-hours) of these batteries. Your available energy will be 8 (number of batteries) x 12V (battery voltage) x Battery Capacity (Amp-hours) and this result will be in Watt-hours. Sometimes batteries will list this number.
Let us assume you have 8, 1 amp-hour batteries. So you will have 96  watt-hours of energy available. This means your batteries can provide 96 watts of power for 1 hour. Alternatively, they could provide 1 watt of power for 96 hours. *Note that this is approximately true, there will be some non linear relationship between the load size and the actual results. Since you should be using only a few restively low power LEDs, this should be a decent approximation.

The wattage of your LEDs. When you purchase LED lights intended for consumer use, they will have a power rating, this is the amount of power you can expect them to consume.
The LEDs in my living room are 5 watts each, and I use 4 to light up the room, so the entire lighting system consumes 20 watts.


So with your 96 watt-hour battery bank, you could provide power to my living room lights for almost 5 hours (96 watt-hours/20 watts).
As far as hooking up your lighting to the battery bank...
They sell LEDs for motor homes/RVs which will operate at 12V. You could also get an inverter to go from 12VDC to 110V AC, and then use normal home lighting, but this will be less efficient as the conversion from AC to DC is an imperfect one.
Good luck!