Centurion lounge does not make sense when flying DL from LGA. It's really not accessible from Terminal C/D. If you're desperate, I know the NYC public buses go from Term B to Term D, then C, they do loop around between B and D, but they don't actually exit the airport. Those would cost $2.75. I have no idea how the free shuttles work or route.
And of course with B6's move to the Marine Air Terminal, the Centurion Lounge is not easily accessible to B6 flyers either (which is a huge disappointment for me).