New Zealand born Aki signed for Connacht in April 2014 from Super Rugby side Chiefs, and has since made Connacht his second home.
Aki was heavily influential throughout the Munster victory and Lam paid tribute to his positive contributions both on and off the field.
Lam said: "Bundee is a Connacht man. He has truly embraced this area. He has embraced the people.
"With Pacific Islanders, everything is around the family and the extended family. It doesn't need to be about blood; it just needs to be the people you care about.
"Bundee always talks about his brothers. He gets in some people's faces at training. He's physical; he wants high standards. He drives that as well.
"He enjoys himself socially as well but, certainly, he has a lot of respect for these guys because he loves this place."
Pat Lam's side went out of the European Challenge Cup in agonising fashion last weekend,conceding a decisive 75th-minute drop-goal against Grenoble.
And the pressure was on to secure their place in the Europe's premier competition, the Champions Cup, after five-point wins for Leinster, Ulster and Glasgow Warriors earlier in the weekend.
But the bonus-point against Munster means that Connacht have completed one of Lam's targets already with two games in the Guinness PRO12 still to play.
"I'm extremely proud," Lam added.
"I said the big goal was to get Champions Cup and it's just such a massive, massive achievement for Connacht to get there. That's ticked off now.
"To go unanswered 29 points sums up what we are about. We didn't start well and we didn't play well at the beginning, but the boys just have a lot of belief in what we are doing.
"I said to the boys, we set the target at five points, but how we go about doing it was crucial. How we did it was a big thumbs up."
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