The Port Authority doesn't operate that way and neither do most airports.
In fact, this is what the PA says about Terminal C
Terminal D
Terminal D was constructed by Delta Air Lines at the east end of the airport. The terminal, which has 10 gates, opened in June 1983. In 2010, Delta Air Lines began to improve the terminal's food, retail, and concessions options, and the Port Authority opened a Welcome Center on the arrivals level, In late 2011, Delta took over the lease of the US Airways Terminal (now known as Terminal C) with plans to expand its operations.
http://www.panynj.gov/airports/lga-facts-info.html
sounds like US is the one who now leases gates from DL.