They have given themselves every chance with this ten tries to three win over a hapless Zebre side and now head to Toulouse in control of their own destiny.
That’s some achievement in a pool which contains two former champions Toulouse and Wasps.
A bonus point at Stade Ernest Wallon, where they scored a shock win three seasons ago, could be enough, a win would guarantee safe passage and one or two other permutations could also work in favour of the westerners.
Dan Robson’s last gasp winning try for Wasps against Toulouse was a big boost to Connacht, no more so than the manner in which Lam’s men defeated Wasps before Christmas at the Sportsground.
Big breaks, but for a side ravaged by injury, warmly welcomed by Connacht.
“We’re top of the pool and we’ve worked hard to be here - Wasps and Toulouse, they’re two champions and we’ve beaten them.
“We earned the right to be where we are now and more importantly going into this game, to have that control in our hands is great.
Prop Denis Buckley is a doubt for the trip to France having picked up a foot injury but there are hopes that out-half Jack Carty will recover.
Lam was forced to go with replacement scrum-half John Cooney at No.10 on Saturday but the ploy worked a treat.
Cooney, believed to be lined up by Ulster as a replacement for Ruan Pienaar, kicked eight out of ten conversions and also scored a try.
They had the bonus point wrapped up by the 29th minute with Matt Healy getting them off the mark after under two minutes.
And while Zebre stunned them with converted tries from flanker Johan Meyer and No.8 Federico Ruzza, Connacht took control with Cooney getting his try before Tiernan O’Halloran and prop Finlay Bealham, the only forward to score, sealed the bonus point.
The ill-discipline of Zebre, which saw winger Lloyd Greeff and tighthead Pietro Ceccarelli binned, saw Connacht open up a 40-14 interval lead with tries from scrum-half Kieran Marmion and returning centre Craig Ronaldson. It remained one-way traffic after the restart as Connacht, mindful of the need to chalk up as many tries as possible, pressed forward.
Healy again scored within two minutes of the restart, while O’Halloran and Marmion also got their second tries.
Replacement scrum-half Caolin Blade completed the rout after Mattia Bellini had crossed for Zebre.
Lam says that only teams finishing in the top seven of the PRO12 should be allowed into the Champions Cup.
His side showed no mercy to a Zebre side who have now only managed a single point from 17 Champions Cup matches.
“The main thing is it’s important that Italian rugby is strong and I think that there’s no doubt Conor O’Shea is making a difference.
You saw the result against South Africa. But I can’t comment too much on that.
Tries: M Healy (2), J Cooney, T O’Halloran (2), F Bealham, K Marmion (2), C Ronaldson, C Blade. Conversions: J Cooney (8).
Tries: J Meyer, F Ruzza, M Bellini. Conversions: Canna (3).
T O’Halloran; N Adeolokun, R Parata, C Ronaldson, M Healy; J Cooney, K Marmion; D Buckley, T McCartney, F Bealham; L Stevenson, J Cannon; S O’Brien, E McKeon, J Muldoon.
JP Cooney for Buckley (38), T Farrell for Ronaldson (43), N Dawai for Muldoon (47), J Andress for Bealham (47), D Heffernan for McCartney (47), J Connolly for O’Brien (50-59), C Blade for Marmion (55), D Poolman for O’Halloran (58), J Connolly for McKeon (67).
K Baker; L Greef, E Padovani, M Bellini, G Palazzani; Canna, M Violi; A Lovotti, C Festuccia, P Ceccarelli; G Koegelenberg, V Bernabo; M Mbanda, J Meyer, F Ruzza.
D Chistolini for Ruzza (37-45), for Ceccarelli (60), J Furno for Koegelenberg (47), O Fabiani for Festuccia (47), A de Marchi for Lovotti (55), D Minnie for Bernabo (60), S Bordoli for Canna (63), C Engelbrecht for Violi (70), G Biagi for Meyer (75).
T Foley (RFU).