I've charged my Mach E without issue, using the Ford provided portable EVSE and a large commercial generator.
Charging the Lightning, you will want to use the Level 1 120v adapter when using the Ford mobile charger. If you want to charge using the generator's 30 Amp outlet, you will want to use a mobile charging cable that is adjustable down to 24A. You may need to purchase an L14-30P to L14-50R adapter since most EVSEs use the 14-50plug. Keeping a 14-30 to 14-50 adapter in your Lightning will give you ability boost any stranded EVs using the pro power onboard.
I have also tested one of those EGO battery power stations to give my Lightning a level 1 charge. It took an hour to deliver 2 miles of range, but it worked.
Charging the Lightning, you will want to use the Level 1 120v adapter when using the Ford mobile charger. If you want to charge using the generator's 30 Amp outlet, you will want to use a mobile charging cable that is adjustable down to 24A. You may need to purchase an L14-30P to L14-50R adapter since most EVSEs use the 14-50plug. Keeping a 14-30 to 14-50 adapter in your Lightning will give you ability boost any stranded EVs using the pro power onboard.
I have also tested one of those EGO battery power stations to give my Lightning a level 1 charge. It took an hour to deliver 2 miles of range, but it worked.