Hi Alan,
There was a William Loveless, b. 20-Jan-1834 SC, d.
11-Jan-1888 Dallas Co, TX. He moved to Dallas around 1858 and his descendants were told that he served in the Civil War.
Unfortunately, Loveless died in 1888 and his wife died in 1875
so I doubt either filed for a pension. Is there any other type of record that can be used to confirm that this man was the "William Lovelace" that served in Co K 19th Texas Cavalry?