Most courthouses do not burn flat to the ground and often some records do survive those courthouse fires.
Have you checked the Family History Library Cataglog?http://www.familysearch.orghttp://www.familysearch.org -- that is the LDS site, click on Library, click on Library catalog.Click on Place Search, type in just Fannin (do not type word county) in first box, Texas in second box.Then you can click and look at the various subjects.
On the Land option there is an index to deeds 1838-1900, that should cover the time period you want.Microfilm can be ordered out on temporary loan to your local Family History Center for a nominal fee.Volunteers that man the FHCs will help you with the ordering, and when the film comes in they will let you know it is in and how long before it will be sent back to Salt Lake City.No charge to use the FHC and they are very friendly in helping researchers.
Check the Fannin Co, TX GenWeb site, use their search feature, type in Lemon about 3 items come up, type in Lemons and several more appear.Many of those are cemeteries, you may find the cemetery where some of your family is buried.
Check around locally where you live, see if there is a local genealogical society, often they offer classes for beginners.Or, see if your local FHC offers any classes to help researchers get started.
Do you know where Jake was born?Do you know when and where any of those children were born?Jake is probably a nickname and I'm not finding him on the census as an adult and head of household.