I winter my Kaffer lime on my covered patio and it's even done fine on nights where in the open it's been 30*-32*F. It is probably a few degrees warmer under the patio roof, but the sides are open to the air and it's been fine.
( I think the new name is Thai lime or Makrut lime. Kaffer, Kieffer and the like are supposed to be non-PC now.)

If yours stays about 40*F it should be even more fine.

We had some 30* temps a couple weeks ago, and my other various citrus on the other side of the house, on my un-covered deck did fine with some minor protection, namely a light cloth draped over them, (an old sheer curtain material) and a single string of mini Christmas lights strung through the branches under the cloth. Turn them on at night and the bit of heat they give was just enough to ward off the chill. They came through just fine.

Barb will trade for viable mature Kaffir lime tree seeds if interested. Thanks.

I would be willing if it is legal in your area. Some areas it's not legal because of citrus quarantine. But I can't figure out how to PM you on this darn site.