I reread LadyL's first post and, maybe I have a strange sense of what constitutes an emergency, but Friend doesn't sound like he has an emergency situation (such as what she stated about staying overnight once if there were a blizzard and he couldn't get home safely). He has a situation where things are a bit tougher (generator instead of regular power and gasoline shortage), but he's not in an unworkable situation (he has a home to go to, rather than having to stay in a shelter, for example). I used to be part of a DAT (Disaster Action Team) for the Red Cross. Friend's situation definitely isn't considered an emergency (I don't know if he would be permitted to stay in a shelter when so many others need to stay in one and he has a home to which he can return). Side note -- we once had a family who wanted vouchers to buy new clothes because they considered themselves to be in need and in an emergency situation due to their clothes smelling like smoke (I think either their or a neighbor's residence had a fire but not a bad enough fire they couldn't return to their residence). Anyway, they were turned down after it was assessed that the clothing just needed to be washed in order to eliminate the smoke, not replaced. They still kept asking for vouchers (turned down again); they didn't want to wash their clothes.
Anyway, looking at it this way, his tougher situation doesn't supersede LadyL's health issues. I think LadyL and LordL should be able to state her medical reasons for not being able to have him stay a week. This would not be rescinding their offer of helping out during an emergency. Again, he's not in an emergency if he still has his home and has a back-up provider for power (this from someone who lived in a house with no gas and no electricity for days, not because of a environmental issues but because my parents didn't pay the bills -- also no fridge and no phone in the pre-cell phone days -- but we still had our house; lack of these things made life tougher but didn't make the situation an emergency for the six of us living there). Friend may feel he's in a true emergency situation for him, but LadyL is, equally, in a true medical crisis for her. With those in mind, LadyL needs to be able to take care of her health. Still, if they want to help Friend saves on gasoline usage, I'd be inclined to say Friend could stay the first night of the week and the last night of the week OR the first two nights of the week or the last two nights of the week (to give LadyL a block of time to continue to recover instead of the time being broken up).