Those would be my guess.

I would think the lemon would be a Lisbon or eureka.

It is so unfortunate that some citrus are not labeled as to specific variety. I suppose most people don't care. So then you can only speculate, but you can narrow it down a bit based on probability.

Lemons would either be Meyer or Eureka. Of those, Meyer is the most commonly sold, since it's very easy to propagate. This year we are seeing Meyer and Eureka in our Home Depot, but they are labeled as such.

As to limes, it would either be Key lime or Persian. Of those, Key limes are most commonly sold by many northern Home Depots. They are quite thorny compared to Persian, with smaller leaves (but unless you see them side-by-side, it may be hard to know). I did see a Limequat for sale at one Home Depot, but that is unusual and was clearly marked.

Key limes and Meyers are typically rooted cuttings. Eurekas tend to be grafted (but not always). So if the plants were rooted cuttings and not grafted, chances are even higher they are key lime and Meyer.

Good luck!

You can also look on the UCR variety database. They have photos and characteristics for tons of trees in addition to photos of fruit, tree, and leaf. I had a few dying citrus trees gifted to me by people who didn't know what they were and I was able to get an ID from there.

Definitely not the Key Lime, I know that one, yes, smaller and thorny. I have Eueka and Lisbon also, and don't mind anther Meyer's', and the Persians are my favorite of all the Citrus.