I am still not following - why would it taking 3 hours to heat the living quarters mean that Li would not meet you needs?
Regardless of the battery chemistry, if you are going to use them in very cold temperatures, it almost always makes sense to heat the batteries. The capacity of all batteries is greatly decreased at low temperature. With FLA at -40F/C you can get about 20% of their rated capacity, with AGM/Gell/SiO2 you can get about 40%. LiFePO4 is a bit better and retains about 50% of its capacity at -40. The other big issue is battery voltage decreases with decreasing temperature and internal resistance increases, so if you are using you batteries to power something like an inverter with a high current draw and a low voltage cut off, you will only be able to use a small amount of the already reduced capacity at low temperatures.
Ideally you would use the heat from the living space or a furnace vent to heat the batteries, but even if you had to use half the batteries own power for heat you would still be better off than using the batteries cold.