98 or 131 kWh battery. OP said long range so 131 kWh.50 Amp circuit at 40 Amps continuous is 9.6kW per hour. I don't know the capacity of the onboard charger in the Lightning but even at increased consumption towing a trailer that is not a trivial amount of kWhs overnight.
Onboard charger will take up to 80 amps needing 100 amp supply to go full power. The included mobile cord is good for 30 amps or 7.2 kW.