Is it acceptable to plant new trees, specifically Crape Myrtles, in the lawn and then place new sod around the base of the tree, or should there be a required distance for a "tree ring" which would include compost and mulch?

This is a bad practice. You will always be hitting it with the mower and string trimmer. This will eventually girdle the plant and cause long term stress or death. If you decide on a tree ring it should be about as wide as the root ball and contain cedar mulch. Keep the mulch away from the trunk, the root flare should always be showing.
Tony M

I've noticed several people pilling up mulch and grass clippings around the base of trees. You suggest not to put mulch around the base of tress. What would you recommend around the base of trees? I personally put some compost or mulch near the base but not very deep. Should I discontinue the practice and if so what is recommended in lew of? Thanks Al

alongwithme-
Please re-read my post. What I wanted to stress is not to put mulch or clippings against the trunk of the tree. This causes the trunk to get and stay wet and invites critters. Let me know if this is still unclear.
Tony M