Your mentioning of Ivan Lawrence, Cass (who went to TX), Alice, Arthur, etc. makes it almost certain that your Ivan Lawrence was Ivan Lawrence Jr., the son of Ivan Lawrence Alexander and Katherine Cox. Per an article on Lewis Cass Alexander of TX, Ivan Sr.'s father was William W. Alexander. I believe that they are the same people that Lee is following.
Get in contact with me by e-mail, and I'll trade data with you and put you in contact with some other descendants of Ivan.