If it doesn't work well, next time try taking off the zest of both the limes and lemons(the skin, but no white, just the yellow and green. The white will add bitter), I use a veggie peeler, but a knife would work just fine too and give you a little more control over depth. Then put them in with the Tito's and shake it every day. Store in a cabniet/cupboard for 3-4 weeks. Then strain out the zest when done.
This is basically exactly how I make Limoncello only with vodka and I also make a simple syrup and add it to the mix after the straining.
Should work fine with out the syrup though, unless you want to add some sweetness to the tito's.
Zest is where it's at.