The Glasgow Warriors coach will replace Cotter as Scotland coach next summer.
"I would have thought he would already have been looking to go elsewhere," former Scotland scrum-half Lawson said.
"The risk of potentially losing Gregor before Vern Cotter had done his bit - had he taken them through to the next World Cup - is now nullified."
Townsend served as Scotland's backs and attack coach for three years, and his Glasgow players have provided a large percentage of the squad under Cotter.
"In many ways he's perfectly positioned to step into that role," Lawson told BBC Scotland.
"He's obviously been in and around the Scotland coaching environment before and naturally the two professional clubs work very closely with the national team as it is.
"He's gone in at Glasgow, taken a year or so to build the squad he wants, the culture he wants and the playing style he wants.
"And by the time he steps in, he'll have had four to five years as head coach of Glasgow and that will stand him in incredibly good stead."
Cotter's future beyond the summer of 2017 remains unclear, though Lawson thinks approaches from elsewhere may have convinced him to move on after his contract expires next year.
"Obviously somebody has offered him the chance to go elsewhere," added Lawson, who won 31 caps between 2006 and 2012. "Whether that's back to New Zealand or elsewhere we'll see.
"As much as we're shocked and disappointed [at losing Cotter], we're incredibly fortunate that we have one of the best and most sought-after coaches in the northern hemisphere, in the shape of Gregor Townsend, to come in and pick up as head coach."
Rory Lawson believes the risk of Gregor Townsend leaving Scotland may have influenced the decision to name him as Vern Cotter's successor.