The Clermont Auvergne boss is due to take up his new post in 12 months time - although his French employers could decide to rip up his contract as soon as Monday.
Whatever the timescale, there is no doubting the new man's credentials after leading his team to the Top 14 crown in 2010 and this year's Heineken Cup final.
A narrow 16-15 defeat to rivals Toulon denied him the biggest prize in European club rugby but Lawson insists the New Zealander is a sound choice to replace former head coach Andy Robinson.
Newcastle forward Lawson - recalled to the Scotland squad for this month's four-team tournament in South Africa after missing the RBS 6 Nations through injury - told Press Association Sport: "I don't know Vern personally at all but from his reputation and what he has done at Clermont, it seems a very good choice.
"I've spoken to guys who have worked with him over there, Nathan Hines and Jason White, and they both speak highly about him.
"I trust the SRU to have done their homework. Clermont were unfortunate not to win the Heineken Cup but they are regarded as being the best team in Europe over the past couple of years when he has been at the helm.
"He's got massive pedigree and I'm sure the boys are out to impress him. He's worked with some top players but now it's up to us to match his standards."
Scotland flew out to South Africa on Friday ahead of next Saturday's match with Samoa in Durban.
They then head to Nelspruit for a meeting with the host nation a week later and a possible encounter with Italy or one of their two earlier opponents will then take place in Pretoria, depending on results, on June 22. Australian Scott Johnston, the Scot's interim head coach, will continue to lead the side on a temporary basis until Cotter arrives.