Have no idea (as I've not done even the most rudimentary research) whether a small lemon tree like this should survive outdoors, but he has now been out for two winters.  We are now just into June, and although he dropped all of his leaves through the winter, and we had quite a late flurry of snowy weather in March, there is now plenty of new growth and he's looking pretty healthy.

I've cut back all of the dead wood and stripped off the old leaves.  I'd like to say this is to increase the health of the lemon tree, and the promote growth to the new healthy bits, but it was mostly to smarten up appearances on the patio!