Kacey, I would prune the lemon this spring when you put it outside. It will put out new shoots -- let those shoots grow so the new leaves will nourish the tree, then prune as necessary again before bringing it inside. This way you'll be able to put it back in the bay window where it seems to be happy.
About this time of the year, mine starts growing new shoots. I let them grow for the most part, and trim them when I prune in spring. I do trim overly lanky growth and use them in cooking.
For fertilizer, I currently just give used coffee grounds dumped in the watering can, some worm compost tea, occasionally small amount of molasses dissolved in warm water, and actual earthworm in each container. During the summer, while outside, I also give ithem hydrolyzed fish fertilizer (Neptune) and AACT. The containers sit directly on the ground and earthworms move in from below. I'm thinking of getting Espoma Citrus-Tone, though, since I'm hoping the oldest of my citruses is reaching possible flowering age. I want to stick with organic fertilizer. Look for Citrus and Avocado fertilizers which will contain the proper macro and micro nutrient mix.
Shelley, I'm not sure why you said yours will never set fruit. It's not likely to flower unless it gets sufficient sun/supplemental light. But if it flowers, they may be pollinated by insects or you should be able to hand pollinate... at least in theory. How the fruit will taste is another story.
She sounds like a fun person.
I use nail clippers to cut the sharp tips off of all my citruses. You can also just pinch off the tips of the thorns of new growth while they are still soft. The citrus leaves are good in Thai style soup as well.