Moss prefers acidic soil, and lyme makes the soil less acidic, so this may have some affect. But probably it will be minor. Find a way to dry the soil out a bit, raise your mower's cutting height, and if possible, prune up any low-hanging branches to increase light levels. All of these things will make the site more hospitable to grass, and less so to moss. Tipping the balance in favor of the grass may do the trick.
in the short term, you can use moss killer. Most garden centers carry it. Use it, rake out the dead moss, then reseed. Meanwhile, the steps above should help the lawn fill in over the long term. Otherwise, the moss will just return year after year if you don't solve the underlying problems.