Sitting below 12 is hard on the battery and you may have already lost capacity to sulfation. Fully charging a low battery with a converter producing 13.6 volts will take three to seven days.
I would disconnect the battery and use that portable as it will usually charge at a higher voltage. Use the recondition or equalization mode if available.
How long will it last with two lights?
We don't now the condition or size of the battery or how many. Neither do we know if the light is incandescent drawing 6 amps or LED drawing 1 amp. And there are other items idling at .3 to 1.5+ amps. Best to just give it a go in the driveway.
The 12 Volt Side of Life