IF you want to go through Memphis and Nashville, you would take I-30 from Dallas to Little Rock, pick up I-40 through Memphis and Nashville, then I-65 toward Louisville, but turn at Elizabethtown, KY onto the Bluegrass Parkway all the way to Lexington.
For my part, I usually do NOT want to go through Memphis and Nashville, but turn north on I-55 at West Memphis, then over to Dyersville, TN and up the Purchase Parkway in Kentucky to join the Western Kentucky Parkway to Elizabethtown and Bluegrass Parkway as above.
This is a frequent route for us from East Texas to Lexington.