I know next to nothing about citrus trees. I need some advice.

Last year I bought a key lime tree for some reason. It is indoors for the winter, of course, but due to go out in a month or so. Since November it has been in a south facing window with six hours of grow light every day. Usually the tropicals are the last to repot, so it would normally get root and branch work in May. It has produced four limes, which make much better gin and tonics than anything store bought.

In early January it dropped about half of its leaves and started up a lot of new growth. Last week it popped out dozens of flowers. Was the repotting window in January? And, obviously,  did I miss it? 

The pot has enough room it can probably go  year without root work. I would just as soon not cut off flowers now or growing limes in May or June. Help?

Not sure if this applies to limes but my lemon tree flowered in December and is currently growing small lemons. It also dropped a ton of leaves. I keep it inside at around 65-75F. I was worried because this seemed too early. I was told that this wasn't a concern as they usually start flowering about this time. I have it in a relatively large pot so repotting wasn't an issue.
Key limes seem to put on flowers and growth in early spring from what I can tell, but you do have it inside, I assume at a mild temperature. After a little googling, apparently the window for repotting is right before the growth period (otherwise, early spring), which evidently just occurred for your tree.
TL;DR: I think you missed the repotting period lol. My guess is that repotting would have to take place as soon as you notice the tree putting on new growth, since you have to keep it inside for the winter and I can't think of any good way to time it for early spring. Best of luck!

There is a nursery near me where they grow a lot of different Citrus, they keep the greenhouse just above freezing in winter, not anywhere near as hot as you are. If you must re pot then you are going to lose fruit, so you have a choice.

Second that. All my citrus trees do amazing in 5 degrees all winter. They are subtropical, not tropical after all. I think you missed it, but it is not that big deal. 

I have been thinking about the same thing. It is time for my first true repotting and root work on them. The last 5 years they have been grown in big pots and been thickening quite good. Nurcery soil still in the inner clump and new compost around it. I think I will take the leap in April. As usual: I will update you if it is a success

This one is from Key West where the record low is 41F/5C. Usually the lows are 60F/15C so I think it does need some pampering.  

The real question was repot this year or wait until next year. I think the answer is next January.