No not prune. Your tree needs to grow more before pruning.

So will it continue to grow like that with a split toward the soil or will it somehow develop a straighter shoot? I want it to look like a tree and it seems to want to grow horizontal...

I have several citrus trees like yours that are fine but will never have a straight trunk. Those trunks are there and in position. cutting them back lower than the branches to encourage a straight shoot would set the tree back 2 to 3 years if it didn't kill it. Your tree has artistic beauty to is structure.

Steve

Do you happen to have any pictures for reference of what it might look like when bigger?

Not a straight trunk anywhere.

Steve

It's your choice really. You can probably leave the lime as a twiggy shrub. Let it follow its natural inclination.

Or you can train it as a standard limbed-up tree with a trunk. Training as a limbed up tree will take much longer, of course. You'd have to select one limber branch to become the upright trunk, and tie it to a stake...gradually tightening the ties over a month or two until it is vertical. Remove all the lower branches. Crop off the top and it should branch out higher up.

In the photo below, the yellow represents the branch selected to be the new trunk. The red lines indicate branch removal. You're not going to like how it looks for a while, but it will get you to your goal eventually -- if that's what you prefer.

Keep in mind that tree-form plants are more top-heavy and must be lashed to a railing or some structure so they don't blow over in winds.

Nice diagram Dave.

Steve

Thanks for the replies, guys! So if I follow Dave's suggestions, would I end up with a straight-ish trunk over time, or is it forever going to be kind of zigg-zaggy? I'm so hesitant to go chopping away at the branches but this is going to sit on my patio and I want it to look like a tree as opposed to a scraggly bush. Nothing wrong with that, just my preference is all. once again, thanks for all the info!

As I mentioned, you'll have to apply pressure to the trunk over weeks to months in order to straighten it. The arrows in my diagram represent the direction they need to be trained/pulled. Hardest one will be the kink at the bottom, but over time it can be reduced. Once you find an appropriate stake, it shouldn't take much work. Heck you don't even HAVE to cut off the other branches. Just Train the leader.

Or just leave the plant to do what it wants. Let it be a bush.