I believe I can tie your Lydia Allen into the Allen's of VA, TN, and MO.William ALLEN (b. 1772, VA) and Mary COPELAND (b. NC) were married in 1793 in VA but they ended up in Overton Co., TN sometime later.An extensive Allen family tree I got recently from Sonia Hacic gives the names of William and Mary's 12 children as follows:
Hiram Mcginnis, Lydia, Elizabeth, Josiah, Nancy, Isaac, Rachel, Sarah [E.], Christina, John [This is John S. Allen, b. 26 Jun 1814 in Overton Co., TN], William, and Stephan.
Notice the strong overlap of names with the children you listed for Beverley and Lydia (Allen) Travis.
Two of William and Mary (Copeland) Allen's children, Josiah and Sarah, married sibling children of William and Rachel (Irons) DALE (Sarah Dale and James Alfred Dale, respectively) in Overton Co., TN.A group of these families moved in about 1840 to MO.
I recently did some research on the Dale's (and Allen's) in Harrison Co., MO.The connections of these families is described in an 1888 History of Harrison and Mercer Counties [MO] and in a more recent (1921) History of Harrison Co. by George Wanamaker.I have more info on the Dale side. Let me know if this sounds like a match.