Hi, I am researching Laird/Lard family also.Our Joab Lard married Margaret Todd the sister of Lydia Todd that John Lard Married. Lydia Todd had one child that I know of Josiah and he grew up in Sangamon county.John married Elizabeth Kelly after Lydia died.In my research I did find another Lydia laird in Missouri, but she was younger.
In checking the census records I have connected Joab to John and to Tabitha because Thomas Lard and his son Dennison were with Joab in Grant County Wisconsin during one census and with Tabitha Laird Jones in another.I am assuming Thomas is a brother, but he may be a cousin.
However, I have not connected John of Sangamon County with Adam and Lucretia Laird.I am still looking for parents of John and hopefully Joab.John's son Josiah names his first son Joab.I know there is a close connection.
I believe that they did have an Uncle Hezekiah that they came to visit.