When my father-in-law came to visit from Romania a couple years ago, he picked up a couple lovage plants at the nursery telling my wife and I that it was a necessary herb for the garden. Well, his two-month visit ended and while my wife can make a good Romanian ciorba-style soup with lovage, it's not something we eat all too often so we had to figure out some different things to do with all the leaves the plants are producing this year.
We have tried it in different things and have found that it can be very good as a parsley substitute in tabouli-style salads. Mixed half and half with mint, was what worked best for us. Lovage has also worked well as a pesto and in pico de gallo (although the lovage flavors can be quite strong for these two uses and could be used in conjunction with other herbs to suit your taste).
Making a lovage simple syrup is also a good way to quickly use up a lot of leaves and is really refreshing mixed with some cold mineral water.
I've actually added a couple more lovage plants to the garden this year since I've found it to be so useful and easy to grow.