Go to Google and put in the words ...William Mars Lemmons Louisiana. You will find a lot more. As was very common at the time, enrolling officers frequently misspelled the soldier's name. Now knowing the incorrect spelling of his name, I imagine the National Archives and Texas State Archives would be able to locate his service record and possibly a pension for you, as well as a copy of the land grant listed below.
I hope this helps.

William M. Lemmons, father of William Mars "Bill" Lemmons

From the General Land Office in Austin, Texas Confederate Scrip Land Grant -- doc. no. CSV 1327 (transcript follows)

The State of Texas | In Commissioners Court Coryell County | Nov. Term A.D. 1881

This is to certify that Mrs. Sarah Lemmons, a bona fide resident citizen of this county on the 14th day of November A.D. 1881, made satisfactory proof that as the widow of Wm. M. Lemmons, who was a private in Captain W. A. Parten's Co. D. 7th Regiment Texas Mounted Volunteers and who died whilst engaged it the military service of the Confederate States at Niblett's Bluff, Louisiana May 21, 1863 is entitled to receive a Land Certificate from the State of Texas for 1280 acres under the act approved April 5th 1881.

Given under our hands & the seal of our court this Nov. 15, 1881.
(commissioners signatures, end of transcript)