The 30-year-old scrum-half was included as one of 11 changes to the XV which recorded an unconvincing 34-24 win over Romania on Saturday, with Allan Jacobsen, Kelly Brown, Max Evans and Sean Lamont the only players retained.
Lawson first captained Scotland in November's win over defending world champions South Africa at Murrayfield and has three wins from three Tests as skipper - a record he is eager to improve after taking over from the rested Alastair Kellock.
The Gloucester number nine is also keen Scotland put their display against Romania behind them and deliver a more accomplished performance in their second match of the tournament ahead of the fixtures with Pool B heavyweights Argentina and England.
He said: "We got a bit of a fright on Saturday against Romania and if ever we needed a little bit of wake-up call, that was it.
"But we came out of that with five points, and now we're looking forward to Georgia.
"We've got to learn the lessons and move on - we want to win all of our games in the pool."
Georgia, coached by former Scotland boss Richie Dixon, have won their last eight fixtures and came close to a shock defeat of Ireland in the last tournament in 2007.
Lawson is wary of Dixon's men, who will have taken heart from the way Scotland's forwards in particular struggled against Romania, but believes a collectively strong performance will deliver a fifth straight success.
He added: "They're going to be four years on, but I believe we've moved on a lot since 2007 and have enough in our armoury.
"Everyone's a cog in the bigger machine. If we all perform our individual roles within that, ultimately I believe we'll be successful."
Key to success for Scotland will be the performances of Lawson's half-back partner Dan Parks and centre Graeme Morrison.
Parks was initially overlooked from squads at the start of Andy Robinson's reign as head coach and Ruaridh Jackson has started five of Scotland's last six Tests, including the Romania clash.
After replacing Jackson in the team, Cardiff Blues fly-half Parks is ready to prove the doubters wrong once more, just as he did when returning to the Scotland side 18 months' ago before becoming an integral figure in a number of key victories.
Parks said: "I'm raring to go. Hopefully I can make the most of the opportunity.
"I feel like I did when I got that chance for the Wales game back in 2010, that same sense of hunger. I really want to do well."
Morrison, likewise, is hoping to impress in his World Cup debut after being omitted from the squad for the 2007 tournament.
The Glasgow Warriors centre was not considered for the Romania clash due to a shin injury, which has now fully healed.
Morrison will be eager to help Scotland on to the front foot against a Georgia team with plenty of forward power.
Morrison said: "The forwards are going to be blowing with the amount of work they'll have to do, so it's up to us in the backline to do some of their work.
"If that means getting the team going forward I'm relishing that role.
"Perhaps it was something we lacked a little bit in the middle stages of the game against Romania."
Morrison will also look to organise Scotland's defence and help the team deliver throughout the match.
He added: "We're going out there, doing Scotland proud, putting in a performance for 80 minutes, instead of 10 at the start and 10 at the end, and ultimately coming away with a good win."
Morrison will line up outside Parks and alongside Nick De Luca, with Rory Lamont joining his brother Sean and Evans in the back three.
Jacobsen is joined in the front row by Scott Lawson and Euan Murray, with a second row comprised of Jim Hamilton and Nathan Hines.
Brown, who moves to number eight, will be part of the back row with Ross Rennie and Alasdair Strokosch.
Strokosch said: "It was disappointing not to play on Saturday, but I'll make up for it this week."
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