Some of the LGA terminals are big, so it would help to know the particular airlines involved. There's a part of Central that's close to the old US terminal (also used by DL), while other parts are farther. I estimate the walk from the AmEx Centurion lounge to the first TSA security checkpoint for DL to be about ten minutes, but there's been some construction along the pathway, so expect detours and more crossing of the roadway than what should be necessary.

IMO this is very tight, but depending on the specifics could be possible.

Has the OP checked MCTs for this connection?