You may never know the exact cultivar but once that fruit matures it will be bit easier to ID
To me the shape of the fruit rules out a Lemon or Lime.

Leaf size makes me think a type of grapefruit.

It looks pretty neglected and with those big thorns it could be rootstock growth. have you check to see if what is growing isnt the rootstock. If you can, try to find a graft and see where the branches start.

Mike

Can you give us more background on this citrus? Also, more photos please? A close up of the fruit, a close up of the trunk to see if this tree is grafted (looking for the graft line on the trunk) as well as where the branches are emanating from (below or above the graft line, to see if you've just got rootstock growing, and not the actual grafted variety), and then a full tree photo? Did you plant it? Can we see a photo of the tag? Impossible to tell by this one photo.

Patty S.

It is difficult to determine an unknown citrus variety. I do not think the fruit is a grapefruit, as the petiole is not correct for grapefruit. It is probably some sort of mandarin. The size of the fruit would back this up. Now that the fruit is starting to color, it will not enlarge much. Looking at the fruit, the technical description would be, "apex depressed areolar area radially ribbed". If you type this description in the Internet for citrus fruits, you might just be able to find it. More help identifying the variety could be possible if we could also see the stem portion of the fruit. Good luck, I'm sure you will need it. - Silica

Ok I snapped a couple of photos earlier.

To give some more background...
-I did not plant this tree, and am sad to say it is squished beside a palm tree. But as long as it is green, I'm just going to leave it.
-the tree is about 10 ft tall or a bit more
-each of those fruits is larger than an orange

I had all of 30 seconds to snap some pics earlier so I'm posting photos of the tag and one photo of the trunk. Branches all seem to come from very low so I suppose it is rootstock (i'm new to all this and actually not familiar with this term but perhaps some of you can clarify).

I will go back out tomorrow and get a picture of the whole tree, and some more pictures of the trunk area.

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To me it looks like a tangreen tree. It looks nice I would leave it alone.

A grafted citrus wouldn't have multiple trunks, so the big branch coming out of the soil on the right appears to be a sucker growing from the rootstock.

It could be even worse than that - it's possible that all those thick trunks are rootstock and only the thinner staked branch is the true variety.
I say that because it could be the original stake tied to the original variety. Is the tag also on this branch? - it's difficult to tell from the photo.
Show us a picture of where that branch meets the ground, from the other side compared to the last picture. Are the leaves on this branch at all different from the leaves on the rest of the tree?
General information: The rootstock is a variety only meant to provide nourishment to the variety growing above it. The rootstock sometimes grows new shoots which should be pruned away. If allowed to grow these shoots can take over and then produce fruit which are not very good for eating.

weird, if it was a dwarf variety rootstock, it wouldn't get that tall would it?

i would say mandarin, by the shape of the fruits.

Crush a leaf under your nose. What does it smell like?