Lawson did not feature as Celtic threatened the most unlikely of comebacks against Artmedia Bratislava at Parkhead, a week after Gordon Strachan's first match in charge ended in a 5-0 defeat in Slovakia.
The 29-year-old will be a more central figure when he makes his first competitive appearance for Motherwell when Russian side Kuban Krasnodar visit Fir Park in the Europa League third qualifying round on Thursday.
Lawson, who joined Motherwell from Ross County, said: "I was on the bench in the qualifiers against Artmedia, when they won 4-0 at Celtic Park. That's as close as I got, so hopefully I can get on the pitch this time.
"It was a brilliant atmosphere, they got four goals and were pushing to the end. It was great to be a part of that night but unfortunately we didn't get the result at the end. Hopefully we can go one better this time.
"It's great to be playing in Europe. The time I spent up the road, you probably think at some point it won't happen. It's something new for me and it's a challenge I'm looking forward to.
"The good thing is we have experienced boys here. It can only help talking to the boys about past trips."
The midfielder made four appearances for Celtic in Strachan's first season but, after loan spells with St Johnstone and St Mirren, decided to move to Ross County for the good of his career in 2007.
Lawson has a Second and First Division title and a Scottish Cup runners-up medal to show for his time in Dingwall, and his impending European debut is further vindication of his decision.
"When I left Celtic, a lot of people see me going to Ross County in the Second Division, and maybe thought that was where I would stay," he said.
"I've worked very hard and obviously the management team up the road and players I played with up there have been a massive help. It's a great reward to be here and be part of this."
Lawson's return to the County team following a four-month injury absence last season coincided with the Dingwall side's surge up the table on their way to a fifth-place finish in the Scottish Premier League.
County's win rate more than doubled in the games Lawson started and he is relishing the challenge of proving himself again.
"We were an unknown quantity last season as a team in general," he said. "A lot of people hadn't seen me play so it was to do so well in the Premier League and great to prove I could play at that level.
"This is another step up and I have to work even harder to get in the team and stay in the team here."