Answer: It's difficult to get grass to grow under trees because the trees cast too much shade, and their roots rob the soil of moisture and nutrients. Grass usually struggles under these conditions. Instead of grass, I'd recommend planting an attractive ground cover that can take some foot traffic. Wild Ginger, Bunchberry, Kenilworth Ivy, Sweet Woodruff, Houttuynia, Lamium or Redwood sorrel.
Lime won't keep moles from tunneling in your yard. They are feeding on grubs so as long as you have garden soil with tasty grubs and earthworms, the moles will visit. The only sure way to eliminate moles is to trap them.
Wish there were an easier approach!
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