Lone Star is the name of the Texas State Flag. It may be an allusion to the former CIA operative and J. Paul Getty Head of Security (/fixer/negotiator) who wore the Stetson or cowboy hat, James Fletcher Chase, since the episode seems to be centered on his perspective.
The origin of the phrase of "Lone Star", refers to Texas struggle for Independence from Mexico, in order to be a sovereign Republic for many years before it joined the United States.