We grow four types of limes - Persian, Kaffir/Makrut, Key and Sweet. We always leave all of our limes on the tree until they are ripe. If you can post some close up pictures of the fruit, I may be able to identify which type you have. Based on leaf shape, I can rule out kaffir/makrut as they have a distinctive double leaf. Are the fruit round (Key) or oblong (Persian)? It is also possible, that it is a meyer lemon. It is hard to tell from the photo.

When you cut them open are they pale green or yellow? Green would be lime, yellow lemon.

Thanks Lynda! Most are pretty oblong though a few are round. But they are bigger than I think key limes would be. I'll tack on some more photos.

And thanks Kate! They're sometimes a bit green inside and at other times more yellow like these in the photo below.

Persian limes are supposed to be seedless for the most part, aren't they? Yours has lots of seeds. And I've read that they are mostly thornless, but I have no experience with Persian limes. My key limes are very thorny.

They look more like a meyer lemon than any of the limes we grow. They are far too big to be key limes.

I just looked at my Persian lime and I think that could be a contender as well. Ours does have thorns, and our fruit is a similar size, shape and color to yours. Unfortunately, I can't remember if it was seedless. I took this just now.

For a reliable, productive lime tree in California, GardenZeus recommends Bearss limes (Citrus latifolia), also known as Persian or Tahitian limes. Like lemons, Bearss limes do not require high heat to mature, making them a better choice for growing in California than true limes. Compared to a true lime, the Bearss lime is larger, has slightly rougher skin, and stores better. It has a less acidic, more mild flavor than a true lime. Fully ripe fruit turn pale yellow, but can be used when green. Bearss limes are generally seedless unless grown near other citrus, in which case they may have one or two seeds. Bearss lime trees are also significantly larger than true limes, with a full size tree reaching 15-20 feet tall, a semi-dwarf tree 8-12 feet, and a dwarf tree 6-8 feet tall. They have beautiful white blossoms. When young, the trees have a fairly open and angular habit which becomes more dense with maturity. They have very few thorns. Bearss lime trees are known to be very productive and can be ever-bearing like lemon trees, but will fruit most heavily in spring. Though evergreen, they are known to drop substantial amounts of leaves in winter.

Looks like a meyer lemon to me. Do the flowers have purple tones?

Thanks everyone. @Ken B Zone 7 I haven't seen any flowers yet but I'll keep an eye out.

Congrats on the house with bonus tree! My vote is Meyer lemon. Do ensure that any growth below the graft is cut away.