Google fun.

[Katy_o]

Wait... Limes don't have seeds? Wtf?!

[Clydesdale Epona]

Wait... Limes don't have seeds? Wtf?!

I had the same reaction when i first read it

[DoraFlora]

I know!!!

One page says,
"Limes without seeds generally have parthenocarpy, which means they are able to create fruit without the need for fertilization. In fruit or plants with this procedure, evolution has removed the biological process that creates the protective fruit from the process that makes the seed. One example of a seedless lime that reproduces is the Persian lime. The seedless Persian lime grows by having its rootstock planted, but only after having a bit of lime tissue grafted to its top will it begin turning into a tree that will eventually bear seedless lime fruits."