Gregor Townsend's side have enjoyed notable wins over Wales, England, France and Australia over the past year or so, and the squad is currently loaded with top-level talent.
The Scots were disappointed to see their momentum halted by last Saturday's 30-15 defeat by the ‘Boks at Murrayfield.
But former Scotland scrum-half Lawson, who has been working as a pundit on Amazon Prime's coverage of the autumn nations series, believes they have shown enough over a prolonged period to suggest they are now a genuine rugby force.
The 40-year-old, who won 31 caps between 2006 and 2010, told the PA news agency: "Historically, we've had one-off performances and wins that grab people's attention and would then get undone in matches we shouldn't lose.
"But Scotland over the past 12 months have won in Wales for the first time in 20-odd years, won at Twickenham for the first time in 38 years and then won in Paris against a really, really good French side.
"You can see genuine progress there. The Six Nations, albeit we lost two games by two and three points at home, was a big movement forward. Gregor now has a squad that has genuine quality and depth, and Scotland know that if they perform on any given day, against any opposition, they will be in the fight.
"No question about it, this is certainly the strongest Scotland squad in two decades, if not more. When I consider the squad now compared to a decade ago, when I was playing, the quality of player across the board and the depth of quality coming through, there are genuine world-class players there.
"The number of British and Irish Lions in the team highlights that. It's a side the likes of which we haven't seen for a long, long time."
Lawson believes the Scots, who host Japan in their final autumn Test this Saturday, will rue the way they played against South Africa.
He said: "Scotland would have been more disappointed with the performance than the result. Gregor Townsend would have viewed it as a great opportunity to see where we are and how close we are to the world champions when we have a good day.
"I think the scoreboard flattered South Africa a little bit but also it just highlighted that, at that level, if you provide opportunities and don't take your own, you can be in for a long afternoon.
"For me, it was a little bit like watching a boa constrictor work on a deer whereby it just gets a hold of it and you watch a slow and painful process of squeezing every ounce of breath out of the victim. That was what South Africa did.
"It will have been a real frustration for Scotland because they wanted to really match themselves against the best in the world by putting their best performance out there, and they were a long way off that."
Rory Lawson was speaking on behalf of Amazon Prime Video for its coverage of the Autumn Nations Series. To watch the Autumn Nations Series on Amazon Prime Video costs £7.99 a month, but new members have a free 30-day trial.