I would think a lime could handle a south facing patio what with the sun/heat radiation to stay warm. I have some plumies in 5 gal plastic pots on the south patio and so far they seem to be fine after a couple years. Not sure I'll risk putting them in the ground any time soon.
My AZ Sweet orange is in a protected area. Sort of a very large alcove created by the wall between my neighbor and me... my west facing house wall. Thrives.
