They can't take credit for having elected LaGuardia if they were only in existence for 58 years, as claimed.
He was last elected in 1941.
They are probably counting the predecessor to the Liberal Party, the American Labor Party. Originally a labor union-New Deal party in the 1030s and 40s, it became increasingly infiltrated by Communists; in the early 50s, the non-communist factions took over the party and renamed it the Liberal Party.