What is my charging (output) capacity from the LT1 as a powerbank? I have 4 * 3000mAh cells so is that 12000mAh, assuming no use of the light?
It’ll bump the voltage to around 5v so current drops. Real test is with a multi-function USB tester multimeter. I’ll guess with good efficiency maybe 9,000mah. Charge it up and drain it under a load until test is done.
You can usually expect to get a little bit over half (~60%) the capacity out of a power bank.
I have a cheap little 4-way USB digital tester but it doesn’t add load 
Take the battery out of a light. Then plug the light in to the lantern, that will be your load.