Karen, it sounds like your tree was overtaken by the rootstock. . .
Kaffir limes have the "figure 8" leaves. Your Kaffir was grafted onto another citrus plant that would tend to keep it smaller; the plant that grows in the ground, the root part, is called "rootstock". Where the two kinds of citrus are joined is called the bud or graft union and will look kind of like a thick widening around the whole trunk, near the ground. The desired tree stock above the bud union will somtimes be growing off at a mild angle from the rootstock.
What happens to unsuspecting buyers is that the rootstock can be very vigorous and sometimes will try to send up it's own leaves and branches. You can tell when a rootstock is doing this because if you examine the trunk closely you will find branches with characteristics unlike the Kaffir lime sprouting from beneath the bud graft/union that I described above. If you don't get in there and pull these little suckers off, they will just choke out the good part (in this case the Kaffir Lime) and keep growing merrily away--and you will think your Kaffir lime tree has done a magic disappearance.
Yes, this root stock can be pretty vicious with 2-3 inch tough thorns that could easily double as nails if you cut them off green and dried them!
So if you try again with a little Kaffir lime tree, ask one of the garden people to show you the bud graft union is so you will know what it looks like and keep an eye out for those vicious rootstock suckers while they are still small. You want to remove them very small because they won't be so thorny. **Pulling them off** is the best way to remove suckers as this also removes other buds around the base of the sucker that might grow into more suckers. Grab the sucker as close to the trunk of the tree as you can and pull sharply downward and it should just pop off if it is small enough.
If you should notice a sucker that has become a dastardly branch of sharp thorns, carefully clip the branch down to a more manageable lenght and then cut the sucker off as close to the trunk as possible. Cut flush with the trunk if you can.
One more thing: should you notice a sucker coming up from ground away from the trunk, dig around it and cut the sucker beneath the surface of the soil and then fill the hole back up.
Citrus can be thorny, but not those giant thorns!
Ya just gotta keep an eye on some of these rootstocks!
