Suzanne,
I don't have pictures as you requested, but I do have the first edition book "Terrell's Texas Cavalry" by John Spencer. It was published in1982. It details the history of Terrell and his regiment and the other two regiments in the brigade. There are a few pictures in the book of officers and locations where the 37th operated. Appendix II gives a short sketch of each company. Company E has one paragraph, but no mention of your ancestors. Appendix III is a roster of the regiment. Your ancestors, A. J. and J. R. Laymance are listed under Company E. A. J. enlisted at Palestine, Tx on July 8, 1863. J. R. was absent sick in the hospital in Houston, but no date is given. No other information is provided on your ancestors. Neither of their names is listed in the Index.

Best of luck on your search.