You’ll want to wait until the lilacs have gone dormant in fall after a couple of frosts and after the leaves have fallen off. Get the hole ready where you want to move them to so they spend a minimum amount of time out of the ground. Amend the hole with Bio-tome starter food. Take as large of a root ball as you can manage when you dig up the lilac being carful that the soil doesn’t fall away. This will rip off the fine root hairs the lilac needs to absorb moisture and nutrients from the soil. Place it into the waiting hole and fill in the soil around it. Make sure it isn’t sunk down any deeper than it was previously. The soil level on the trunk should be exactly the level that it was previously. Dirt or mulch piled against the bark slowly strangles the plant. Tamp down the soil and water it in thoroughly to remove any air pockets from the soil and keep it moist until cold weather arrives.