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."

The hosts led when Harrison ran onto a long goal kick that had bounced over Cambridge keeper Josh Coulson, and tapped the ball into the net.
Ben Williamson hit the post for Cambridge as they looked to level.
Stevenage sealed the win when Connor Ogilvie's drilled cross found Harrison, who converted from close range.
Harrison helped Stevenage secure promotion to League One in 2011, and is back at the club on loan from Chesterfield.
Stevenage caretaker manager Darren Sarll told BBC Three Counties Radio:
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"It was a good performance. We've come away from that knowing that that's still not our best. There's still so much to do in terms of improving us.
"There's real signs of the old Stevenage coming back. Standing shoulder to shoulder, and we won't be beat. I love that mentality, that's the mentality that I've been brought up on here.
"I thought we could have done better in the first half. To be a little more authoritative with our football, to go after Cambridge a little bit more than we did. There's lots to be pleased with, more so the fact we can beat sides above us."

The Class 700 Desiro City fleet is intended to ease overcrowding on the north-south route from Bedford to Brighton through central London.
Initial testing will be carried out at Three Bridges depot, then on the Brighton line before the train carries the first passengers next spring.
Thameslink said the new trains would transform the service for passengers.
The Class 700 trains will each have 12 carriages, instead of eight on many of the existing Thameslink services.
An extra 1,000 rush hour seats are promised between Brighton and London and 80% more peak seats across between Blackfriars and St Pancras in central London.
"The doors can open far more widely and people can get on and off the train more quickly, which means it can depart punctually," said Ruth Humphrey, project manager for Siemens which is building the trains in Germany.
All the new trains will be in use by 2018.
As well as the current Thameslink network and the Wimbledon Loop, they will be deployed across new routes from 2017 as part of Â£6.5bn Thameslink improvements currently under way.
Meanwhile, Chancellor George Osborne has said he is committed to a full study into building a second main line from Brighton to London (BML2).
The government has already said it will provide Â£100,000 for a new study into the reopening of the Lewes to Uckfield line in East Sussex.
In a letter to Conservative MP for Lewes Maria Caufield, Mr Osborne said he had extended the Lewes to Uckfield study, which would now also look at improving links between London and the south coast, including a feasibility study on BML2.
Rory Lawson believes the risk of Gregor Townsend leaving Scotland may have influenced the decision to name him as Vern Cotter's successor.
[NEXT_CONCEPT]
Byron Harrison scored twice on his return to Stevenage, securing their first home win since November.
[NEXT_CONCEPT]
The first of 115 new trains for the Thameslink network has arrived in West Sussex to begin tests.