moss in lawn
Moss thrives on the shady, acidic soil under your oaks and pines. The lime was an effort to make the soil pH more alkaline, but with oaks and pines, you can never apply enough lime to change your pH that much. Given the right conditions, grass can outcompete moss, so your plan should be to improve your turf. Consider having your lawn power raked, which will break up the surface and tear up some of the moss. Overseed thin or bare areas. Then fertilize your lawn once or twice a year to promote healthy turf.