You're right. I thought 1872 was too early for Dalhart. The town didn't take off until the railroad was built and went through there. Mr. Lawley likely stated his town of residence in 1903, not birthplace.
I've seen the James E. Lawley record you mention. Unfortunately, there appear to be up to half a dozen James Lawleys born around 1870. So it gets difficult... and with our James Lawley incorrectly listing his birth town, even more so.