Among the over 110 cultivars of Citrus we grow, primarily in the ground, in The Woodlands, TX (about 30 miles north of Houston, supposedly USDA Zone 9b) is a roughly 10-year-old Persian Lime in a large container.
Although still subject to freeze damage in the upper 20s F or lower, Persian lime trees are slightly more winter hardy than Key/Mexican lime, and they produce larger fruit in much greater quantities. Unlike seedy Key/Mexican limes, Persian limes are a naturally occurring triploid, so in theory they cannot produce any viable seeds. In practice, I typically find 1-2 seeds for every 50 or so homegrown Persian limes I juice. (As the great Yogi Berra once said, “In theory there is no difference between practice and theory, but in practice there is.”). 
Here is the only viable seed I found in a batch of 50 home-grown Persian limes:
I have grown out several seeds from home-grown Persian Limes in the past, but none are fruiting size yet.
Two days ago I harvested 50 limes from our 6’ tall tree (out of about 80 total on it this year):
I washed them and started a batch of “Lime-cello” from their zest, made 2 lime pies for Thanksgiving, and froze 32 oz of juice as cubes for future use. FYI, although I typically use home-grown Finger lime juice vesicles, these 2 pies are each topped with a home-grown Lemondrop (lemonquat) slice “twist”.
Like to use limes for cooking or drinks? Do consider growing a Persian Lime tree, but keep it in a pot to move indoors temporarily if a freeze threatens!