The reigning Pro12 champions start their campaign against the tournament’s most successful side when four-time winners Toulouse visit the Sportsground on Saturday.
The domestic sides floundered in the Champions Cup last season, but Lam reckons they can bounce back and cause a few shocks against their English and French rivals this term.
“Without a doubt (the Pro12 teams will challenge), we’re all spread throughout the competition. And everyone’s determined,” said Lam.
“Glasgow will be better, the Irish provinces will do a good job. We all feel that sense of responsibility, there’s no doubt, talking to the other coaches, Wayne Pivac at the Scarlets too.
“The added bonus is there’s four chances for the Irish provinces, and we want to make sure we’re there.”
None of the Pro12 sides qualified from the pool phase of the Champions Cup in 2015-16 with Ulster the best finishers in ninth position overall. But Ulster were 10 points behind eventual champions Saracens in Pool 1, while it was a terrible campaign for the other Irish provinces with Munster finishing third in Pool 4, and Leinster ended up bottom of Pool 5.
Connacht fell in the quarter-finals of the Challenge Cup away to Grenoble last term, but for the first time they have qualified for the top competition off their merit.
But they will have to face their first game back in the Champions Cup without hooker Tom McCartney (hamstring) and wing Matt Healy (hand) both out of action until the end of November.
Prop Denis Buckley (knee) is also out until November, while Ireland international lock Quinn Roux has concussion and is undergoing the return-to-play protocols.
Fellow international scrum-half Kieran Marmion remains a doubt with a calf injury while Eoin McKeon (chest) and Peter Robb (hip) are both rehabbing.
Connacht have been boosted by the return of former Ireland U20s captain flanker Sean O’Brien, who picked up an ankle injury in pre-season. Eoin Griffin (hamstring) and Rory Parata (knee) are also set to re-join training. But Lam is concerned about the chances for Roux, who was injured at Carton House.
“It happened in Ireland training, it was really innocuous, he hit his head on the floor,” he said.
“All the guys, except for Tom, Denis and Matt, they’re being monitored by the medical staff, through training. Hopefully they’ll be available.
“You want Quinn, Ultan Dillane, Andrew Browne, different types. As a coach you want those different bullets you can fire, ammunition. Which is why I want as many of them back.”