From Ground: When the lemon thyme plant is growing directly in the ground, first, water the plant thoroughly to hydrate it and soften the hard soil surrounding its roots. Next, dig a generous circle around the plant using your garden spade. The circle should be of such diameter that it doesn't damage the main root system of the plant. Gently lift the plant, keeping the root clump together.
From Pots or Seedling Trays: Before removing the lemon thyme plant from a pot, make sure that the soil is not bone dry as it may crumble damaging the roots. Water the plant a few hours before you plan on transplanting to moisten the soil. Then, tilt the pot and gently tap its edges. The plant should slide out with its soil and roots intact. If grown in seedling trays, push the seedling out from the bottom, carefully holding its stem.