Amps x Volts = Watts.
Some napkin math:
An AC runs, give or take, 10A at 120V is 1200W. Let's say it cycles on 50% of the time. 9pm to 7am is ten hours, five hours of run time so you're talking 6000Wh. That's 500Ah at 12V.
Since you are lead acid you shouldn't discharge your batteries beyond 50% so you would need 1000Ah worth of batteries.
If you need to make 6000Wh with solar in an 8 hour day of good light you will need 750W of solar power. If you have a 2000W generator putting out 1600W continuous you can do it in just under 4 hours, in theory.
It's actually more, but I won't start the battery charging profile discussion right now. Let's just say that due to the characteristics of lead acid batteries the serious boon docker should plan on running his lead acid batteries between 50% and 80% SOC (State of Charge)..... So your really would need about 800Ah so a 1600Ah battery bank....
Of course you also need electricity for other things. And there are losses. An inverter gets warm. This heat comes out of your budget.
I have done the above on a boat. 4-250Ah AGM's (600 pounds worth of lead) paired with a 1500W inverter running a 6000BTU AirCo. (Half the size of the average RV AC) If it wasn't too hot and it didn't run too often I was able to get 8-10 hours out of that bank, which was dedicated to this. I had another bank for the rest of the house.
Lot of weight, not enough roof.
Also illustrates the true value of LiFePO4 Less weight, more Ah per volume, higher possible discharge rates, higher possible charge rates.
Learn how to do the math and then you can build endless "what if" scenarios for YOUR needs instead of getting some good and a lot of useless info here.
'20 RAM 3500 Long Horn '20 Heartland Road Warrior 430 https://thecastle.blog/
Before:'17 Berkshire 38A class A https://dragonship.blog/
'11 Heartland Cyclone TH, '11 Lance TC, '05 Keystone TT, '76 Coachmen class A and a '16 DIY Transit conversion........