Hi Jared,
Most lemons are pretty hardy and can take temps down to freezing (32*) but key limes are tropical - if the temps get much below 40, it will be toast. I am assuming your Mother lives near/with you? Not exactly citrus growing country so those puppies will need to come in for the winter. Also, because citrus are tropicals, they will need light (as in grow lights) because the bloom time is before the frost free date. You may also have to hand pollinate (or invide some bees in for the winter).
Most citrus bare fruit in the first 7 years. The good part is that they take to pruning very well. To keep them in pots, pruning (root and top) is a must. Key limes make great potted plants but lemons are a little rambunkshus. It will take some work to keep it in hand. Your next citrus-in-a-pot should be a kumquat. Yum-Yum!
My daughter (Zone 6) is growing Kumquat, Key Lime, Yuzu and Mandarins in pots in a temperate greenhouse. She heats to keep it above freezing and is producing enough fruit to keep her happy.
Citrus are heavy feeders so citrus food is a must. I had to buy a bag on my way through California for my daughter. Its not carried at Home Depot around here.
A doable fun project.
Daisy