Alas, I see this is an older post, so I hope you are still checking this email!
The Thomas Lynch in your list was my gggggrandfather by his second wife, Maria(h) Jane Powers.
I found some digital copies of The Northern Standard Newspaper online. In one publication, published on 8 Apr 1846, Thomas Lynch and James Welch (I assume James was his brother-in-law) had posted a notice of a horse appraisal they had completed. I believe you can access the page by this link:
http://texashistory.unt.edu/ark:/67531/metapth80587/
Also, there are several notices on various days throughout the year 1850 listing Thomas Lynch as having mail being held for him at the post office.
I believe that Thomas Lynch moved to San Saba County, Texas, and died there in 1899, where he is buried in Varga Cemetery.
Since this posting, have you discovered anything about the parents of Thomas Lynch? Have you any photos of him or his children by either Elizabeth Welch or Maria Jane Powers?
Thomas Lynch, Jr., aka "Tom Lynch", his son by Maria, is my ancestor.
I hope this helps you fill in the blanks a little.
Blessings!