The Scots flew out from Edinburgh on Friday afternoon bound for Johannesburg ahead of a four-team tournament starting next month, with Newcastle Falcons forward Lawson a late call-up to the squad.
The 31-year-old missed this year's RBS Six Nations campaign through injury and his last outing for his country was the humiliating 21-15 defeat to Tonga in Aberdeen last November. He told Press Association Sport: "My last game for Scotland isn't the happiest memory I have and I want to put that right."
Lawson added: "I got injured just afterwards and missed the Six Nations and that defeat to Tonga is not how you want to bow out. It sticks in the back of my throat. So it's good for me personally that I have now got the chance to rectify things. I didn't want that game to my last for Scotland."
The Dark Blues face Samoa on Saturday in Durban before heading to Nelspruit for a meeting with the host nation a week later.
A possible encounter with Italy or one of their two earlier opponents will then take place in Pretoria, depending on results, on June 22.
Lawson - who will move to Newcastle this summer after quitting former club London Irish - hopes to play his part after ankle ligament damage in the run-up to the Six Nations cost him his place.
But he has been given his latest opportunity after front-row rival Ross Ford suffered an injury blow himself.
"You want to be part of that success, don't you?" he said. "I'd have been even more worried if I had missed this trip, another three or four weeks as a squad, not being part of it. Being out injured was tough.
"I missed the Six Nations then was left out of the initial squad for the South Africa trip. But now I'm here I'm delighted to back and just want to get back on the training field."
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