Hello! I live in Phoenix Arizona and I'm moving into a new home that has a lime tree in the front. I've had experience caring for other fruit bearing trees but never citrus before. So I was wondering if you could help me identify the kind of tree this is and point me in the direction of any helpful care guides. I was told it was a lime tree but when ripe the fruit turns yellow. The fruit has a mild lime taste that is also a bit floral and slightly sweet. It had large thorns on it as well. The searches I've done have suggested that its a Mexican lime tree but I can't find anymore information about it. Also it appears that there's a dead branch in the center. Im not sure when a good time to prune it would be. Any suggestions on what it is and how I can care for it would be very helpful. Thank you!

You can remove the dead branch at any time.
It looks like the rootstock has taken over, at least partly, from the grafted variety. Check the fruit on all the various "trunks" and see if they are all the same. The fruit is the wrong shade of yellow for a Mexican Lime.

You have a combination tree: part root stock and part (maybe) lime tree. Look at the leaves on each trunk - different citrus sometimes have different leaf shapes.