2,4-D broadleaf weed killer is an option. In theory, 2,4-D will not kill daylilies. Daylilies are monocots just like grass. Most of the weed&feed products for your grass contain 2,4-D.
When I use 2,4-D (spot spray), I try not to get it on any daylilies, but if I do, it seems ok.
If you are using concentrate, proper dilution is important. A "strong" mixture of 2,4-D will kill everything. I know this from experience.
also, my experience has been that 2,4-D seems to work better on thistle than round-up. And, it's a lot quicker.