My best wishes go out to all employees affected by the shutdown of Lynx.
I unfortunately believe the same thing would have happened if It would have been Southwest instead of RAH. Southwest Airlines doesn't have a spotless history either when it comes to codeshares, mergers and acquisitions. A number of years ago when ATA went bankrupt the first time (2004), SWA took over most of the midway slots in a codeshare agreement. ATA at the time also owned a commuter carrier, Chicago Express that was abruptly shutdown (March 2005) quickly after the deal putting over 150 pilots and almost 450 other employees put out in the street.
Then ATA went bankrupt again in 2008 and Southwest purchased that airline. Towards the end of November 2008, Southwest announced it was buying the operating certificate and the remaining assets of ATA Airlines. This acquisition transferred to Southwest Airlines ownership of New York LaGuardia slots formerly controlled by ATA. The transaction did not include any aircraft, facilities or employees of ATA. (Source
News Release) Again many good people left out on the street.
Southwest has been a successful airline in the industry, but they do not have the greatest track record in terms of helping people maintain their jobs. I think had they bought Frontier they would have in the least shutdown Lynx and probably done it even faster than RAH.