The SPL clubs appeared to reach an impasse last year after failing to reach agreement following a series of meetings which saw a proposal for a 10-team top flight and 12-team SPL 2 rejected.
Lawwell is aware the 10 non-Old Firm clubs have met in secret with a view to changing the 11-1 voting structure, which favours Celtic and Rangers, to a 9-3 format and he called that move "divisive".
However, on the specific topic of league size, Lawwell claims the Parkhead club are amenable to a bigger SPL which would incorporate a split and see the top clubs play two fewer games per season.
"If we were asked our opinion on whether we want a 10, 12 or 14 (team league), we could see ourselves voting for a 14 as long as it's a six and an eight and if that helps the clubs that have great concerns about relegation," Lawwell told STV. "We actually started at the strategic group with a 10 (club plan). We felt it was right. It was 36 games and that gave us the appropriate time for Europe and possibly a winter break.
"Martin (Bain, former Rangers chief executive) and I were then convinced for a 14 because the top six would play 36 games. We were persuaded to go back to the 10 for the greater good because the majority around the table wanted the 10. But 10, 12 or 14, it doesn't really matter, other than the number of games you play."