This marriage bond was taken out in Mercer County, Kentucky in 1847 by John Lake and Thomas Brown in preparation for the marriage of John Lake and Charlotte Brown. The image used in this blog post was made from a digital image of the bond that was located on FamilySearch.
John Lake is signing for himself. Thomas Brown is signing for Charlotte. There's no direct statement or indirect information here regarding the relationship between Thomas Brown and Charlotte Brown. The fact that he has the same last name as Charlotte and that one party on a bond usually signed for the groom and the other party usually signed for the bride suggests a relationship. Thomas could have easily been Charlotte's father, uncle, or brother. The law wasn't concerned about the specific relationship between the Browns. The law was concerned that he could vouch for Charlotte's age and eligibility to marry.
The best plan of attack at this point is to review 1840 and 1850 census enumerations for the Lakes and Browns in Mercer County, Missouri, for John Lake and Thomas Brown. It is worth noting that there's no guarantee that either man is in the county in either of those years.