Best way to use the rest of a lemon after grating off the zest?

I haven't tried this myself yet but I thought the idea from Imperfect Produce to use citrus peels to make a homemade cleaner (by soaking them in vinegar) was a good one. Not sure if the effectiveness is diminished if they've been zested! http://blog.imperfectproduce.com/blog-1/2018/1/10/how-to-turn-your-citrus-peels-into-a-non-toxic-kitchen-cleaner

The simplest way to use the lemon or limes for that fact is to slice thin and add to a pitcher/jug off water, chill, drink. Will even flavor a refill to the pitcher. If you don't have time to do the following, put in a zipper freezer bag, freeze for later use. Then take a few slices of the leftovers, add to a bowl of water, heat to boiling in microwave, let cool several minutes, remove, wipe microwave oven down. They will clean and freshen the oven in the best, easiest, most natural way possible. If you have any strong odors in the oven they will disappear!
Even though I compost all vegetable matter, I also put a few things down the garbage disposal, it doesn't take much for an odor to develop. I put the leftovers on top of several pieces of ice in the disposal, running first cold, quickly switching to hot, while running disposal. The ice sharpens the blades, the citrus cleans and freshens the disposal. No waste!

Put it in a zipper bag and refrigerate or freeze. Once you have 2 or 3 boil them until you have lemon mush. Add sugar and water dissolving the sugar completely and you have have lemon simple syrup. Use it in iced tea, ho tea, lemonade, sangria or whatever you like.

Or juice it and freeze the juice in ice cube trays --pull out and use as you need fresh lemon juice in the future.

I usually wrap and refrigerate it - rarely a week goes by that there's not some way to use lemon juice. A pan sauce, salad dressing, braise, vegetable dish, dessert....more often than not, I find the missing element in a recipe is that hit of acid. Fresh lemon juice never goes to waste.

Or make a glass of fresh lemonade: place juice in a tall glass. Add a few spoonfuls of sugar, to taste. top off with cold water or seltzer, some ice and a sprig of mint or basil.

You can wrap the lemon in plastic wrap and toss it in the refrigerator for later use. Depending upon the type of wrap, it could keep just as long as if you hadn't removed its natural protective layer.

One idea is to make icing from the lemon juice and icing sugar. It came to mind because you said you are baking and I haven't met the person who doesn't like lemon icing.