I started at both ends... by researching Mattie and also by researching William Clark and Meriweather Lewis. What I was hoping is that by staring at both ends, I could try to narrow down the possible relation connections and/or find a link to Mattie via the known descendants of either man. That didn't work out as well as I'd hoped.
My great grandmother, Mattie Clark, was born 2 Jun 1878 to Jam Clark and M Parmellia Lewis Clark in Tennessee.  She does not have an official birth record or a delayed birth record with the state of Tennessee. As of the time of her death, she had the following half brothers and sisters : Ed Clark, Nashville, Mrs Myrtle Bateman and Mrs EJ Wyatt, Erin, TN and Mrs L O Rye, Birmingham, AL. John Clark, Tennessee Ridge, TN . Being that the males have the last name Clark, these half siblings are likely her father's children with a different mother and are most likely born after the 1880 census in which James appears with Mattie's mother.
Mattie was married twice.  First, she married James Walker on 12 Jan 1896.  Her name became Mattie Clark Walker. Mattie and James had children including two sons, Herman and Elvis   and two daughters, Alma  and Mary . Alma was 3 at the time of the 1900 census, making her born about 1897 and Herman was 1, making him born about 1899.  James predeceased her by about 50 years so he died in about 1907. 
On 11 Dec 1911, presumably after James' death, Mattie Clark Walker married Andrew (Andy) Sinks, my great grandfather.  Children from this marriage were Nellie (Nell) Sinks, John Michael Sinks (my grandfather) and Eugene Sinks.
Mattie died on 30 Mar 1957 in Nashville, Davidson Co., Tennessee, and was buried on 31 Mar 1957 in Erin, Houston Co., Tennessee, USA. 
Several family members told me a story about going to put a grave marker on Mattie's grave long after she was buried. My aunt told me the story in my phone interview with her :
"I remember one time when mother and daddy ... we were in TN and we went on a three or four day excursion to find where his mother was buried and found some cemetery way way back in the hills. We had to call some man to find this cemetery and it was something else. I don't even know how we did it. But supposedly, my uncle, which I guess I could call Laura Belle my aunt... Daddy gave him some money to go and put a headstone on his mother's grave. Or redo the headstone. But we did find her grave. It was way, way deep in the woods. I'll never forget it. I lived in Tennessee at the time and I mean it was way in the back woods. I knew somebody who knew somebody who knew somebody and that's the way it went. And that's been 30 years ago." I later found that cemetery way out in the hills (Cedar Hill Cemetery) and Mattie's gravestone. The new gravemarker that my family placed on her grave can be seen on Mattie's find a grave profile. 
What I know of Meriweather Lewis and William Clark is from historical research rather than genealogical research. Of the two, Meriweather Lewis is the easy one. He never had children. People who are related to him trace their genetic roots back to his sister Jane, at best. Although there are questions about how he died, there are no outstanding paternity questions that I am aware of.  William Clark, however, married twice and had eight children. 
So, that left me with one of three options in connecting our family to Lewis and Clark... the variety of which do not help me narrow anything down. Either 1) our family is not related to either one of them, 2) we are one of the families who claim relation to Meriweather via his sister, Jane or 3) we are related to William.
Had Mattie's surname situation even been any more specific, I might have been able to use this information to narrow down which one we were related to. But Mattie's father's last name was Clark and her mother's maiden name was Lewis. It is a comedy of directionless searching.
I have done quite a bit of research on Mattie's parents. I know that Mattie's father, James Clark, was born about 1842 because of his age in the census that Mattie shows up on with him.  Unfortunately, there were many James Clarks born around that year in Tennessee. I also know that her mother would have been born around 1849 because of the same census.  However, there is no record of a Parm Lewis. If I use Missouri, there is a Missouri Lewis born about 1849 in the 1860 census taken in two different districts (district 5 and district 14). Without additional information about my Missouri Parmellia Lewis, I can't narrow it down to one of the two families.
Here is what I know about Mattie's parents :
- Her name was written as "Massour Parm" on the 1880 census.  In Mattie's obituary, it was Parmellia Lewis. In the marriage record, it was M P Lewis  There are two Missouri Lewis's in census records that match her age. There are no other female M Lewises that match her age that I know of in the area census records. So it is likely that her full name was Missouri Parmellia Lewis.
- 1849, she was born - based upon her age in 1880 census 
- 1875 Married James Clark 
- 1878 Mattie born 
- 1880 census with Mattie and James Clark 
- her death would have been between 1880 and James' remarriage
- He is listed as Jam Clark in Mattie's obituary 
- born about 1842 
- 1875 Married Parm 
- 1880 james Clark in census with Mattie and MP 
- James Clark re-marriage 1880- ? - assuming remarriage because Mattie was survived by 5 half siblings, the males of which, have the Clark last name so they were half siblings via her father.
- James Clark had at least 5 more children at least 9 months apart each, we'll round off to at least 5 more years of life after his remarriage. I am guessing these children are born after Mattie because Mattie was 79 at her death so it would have been quite the stroke of luck to have 5 siblings survive her that were old enough to have been moved out at the time of the 1880 census when she was 2. So it's my assumption that they are younger half siblings. 
- James clark died 1885- ? - there are some death records without birth dates for James Clark +- 10 years from 1890 but they lack details other than street addresses, which I don't have for comparison.
I would love to know if anyone has found a connection to this family that might yield more information about Mattie and her ancestors. Information about her or her ancestors could potentially be found in Walker, Lewis, Clark or Sinks families. I can be contacted in the comments below.
- living aunt, phone interview, 12/19/2012.
- "Mrs Mattie Sinks Dies in Nashville After Long Illness". Stewart Houston County Times, Dover, TN. April 9, 1957.
- "Mattie Clark." Find A Grave - Millions of Cemetery Records and Online Memorials. 11 Oct. 2007. 09 May 2013 <http://www.findagrave.com/cgi-bin/fg.cgi?page=gr&GSmid=48121560&GRid=35433012&>.
- Death Certificate for Mattie Clark. State of TN State Department of Health Division of Vital Statistics. Death Number 57-05482. Informant : Mrs. Janet Lewis of Nashville, TN. Note : the informant signature is not clear
- "Tennessee, Marriages, 1796-1950," index, FamilySearch (https://familysearch.org/pal:/MM9.1.1/X8BC-1QT : accessed 01 Oct 2013), James Walker and Mattie Clark, 12 Jan 1896.
- "United States Census, 1880," index and images, FamilySearch (https://familysearch.org/pal:/MM9.1.1/MD7J-6DR : accessed 01 Oct 2013), Mattie Clark in entry for James Clark, 1880. Notes : This is the only evidence I have of the Missouri Clark connection. This census entry is indexed as Masour P Clark as mother's name. I have not yet seen the original. Everywhere else references her as Parmellia or Parm so, whatever her first name was, she likely went by her middle name
- "United States Census, 1930," index and images, FamilySearch (https://familysearch.org/pal:/MM9.1.1/SPHW-MGH : accessed 01 Oct 2013), Andy Sinks, 1930
- "Tennessee, Marriages, 1796-1950," index, FamilySearch (https://familysearch.org/pal:/MM9.1.1/X812-1WB : accessed 01 Oct 2013), Andrew Sinks and Mattie Walker, 11 Dec 1911.
- "United States Census, 1920," index and images, FamilySearch (https://familysearch.org/pal:/MM9.1.1/MNR3-5NM : accessed 01 Oct 2013), Andrew Sinks, 1920.
- "Tennessee, State Marriage Index, 1780-2002," index, FamilySearch (https://familysearch.org/pal:/MM9.1.1/VND4-4JK : accessed 14 May 2013), James Clark and M P Lewis, 1875.
- "Tennessee, Death Records, 1914-1955," index and images, FamilySearch(https://familysearch.org/pal:/MM9.1.1/NS8H-KK3 : accessed 01 Oct 2013), Jas Walker in entry for Sinks, 1931. Note : The name 'Alma' could be any name that fits Al__a. The date on the death certificate appears to be Oct 3 but it's scribbled and unclear.
- "United States Census, 1900," index and images, FamilySearch (https://familysearch.org/pal:/MM9.1.1/MSD9-763 : accessed 02 Oct 2013), James Walker, 1900.