It should, but spread the lime asap. It takes a good 6+ months for lime to make any difference. On the other hand, 5.5 isn't really terrible. The Durana Clover that I sell does very well on a pH of 5.5. Most other clovers do better at 6+. I'd be more concerned about doing a spring planting than your pH.

If it was me, I'd spread the lime now or early spring and plant it next fall. That does a few things for you. One, it reduces your weed competition because the fall frost will kill most weeds but not your clover/chicory. Two, it gives your clover an extra 6 months to put down roots before its first summer stress. Three, it will give your lime more time to work. Good luck.