The Gers will play in the second tier next season after winning promotion from Scottish League One, and Lawwell claims that their journey through the divisions will make them a better side.
"I think they are in real challenges financially, but the fundamentals of Rangers and the Rangers support are strong; in terms of the size of support, the facilities they have, and that will bring them back," Lawwell told BBC Sport.
"Rangers will return, I'm sure, as a much stronger force in Scotland in the coming years. I think the fundamentals of Rangers are strong; and I mean their support and the fundamentals are strong against Celtic.
"So, I believe that, through time, Rangers will be a much stronger force in Scotland than they are at the moment."
Celtic clinched this season's Scottish Premiership title on Wednesday evening with a resounding 5-1 win over Partick Thistle.