The Edinburgh outfit expressed an interest in taking over the ailing SPL side's footballing operation for the rest of the season.
But it is understood a proposal for Spartans to start next season in the Third Division is unlikely to succeed as the Scottish Football League would not grant automatic membership. Instead, Spartans would have to go through an application process if Gretna fold.
Lawson said: "A couple of months ago we met SFA chief executive Gordon Smith to talk through a pyramid structure, long before the Gretna situation came to the fore. Obviously, if there is a chance Gretna fold we'd be among senior teams trying to get into the league.
"We've beaten Alloa, Berwick and Queen's Park in the Scottish Cup. Beating teams on a one-off is different to a weekly basis but I'm sure we can go into the Third Division and do well."
SFL chief David Longmuir has stated previously that any move by Spartans or another club currently outside the professional ranks, would have to be examined rigorously.
"In any set of circumstances, the SFL would carry out a proper and thorough application process for the admission of a new team into our set-up," said Longmuir.