Lamb joined Italy's preliminary panel before the World Cup, and did enough to impress coach Kieran Crowley to make the official squad.
After winning their opening two games in France, spirits are high in the Italian camp ahead of Friday's match against New Zealand, as Lamb told Reuters in an interview.
"The mood is very positive. We set out three or four months ago to win the first block of games with Namibia and Uruguay.
"We've done that, we've got ourselves 10 points to give us the opportunity of facing the next two games with confidence."
Lamb only made his Italian debut in August, but playing for Italy had long been on his mind.
"It's always been in the pipeline as an opportunity.
"My father was born in Turin, he's 100% Italian and growing up, my Italian grandmother lived nearby, there's always been an Italian influence in my life."
In 2016, Conor O'Shea became Italy coach, after his spell at Harlequins, the club where the young Dino Lamb began his career, and still plays.
"Conor knew about my Italian links, and asked me to keep an open mind about it, but at the time I was involved in the England underage setup and wanted to see that through."
Last December, Lamb spoke to Crowley when the coach came to watch him play.
"I didn't want to just turn up because of my Italian background. I needed to know I had something to offer the group," Lamb said, and he quickly showed his worth.
He played in three of Italy's warm-up games, scoring a try against Romania. In France he followed that up with another try in his first World Cup game in Italy's win over Namibia.
"It's a rare occasion for a lock to get over the try line," Lamb said with a smile. "I was very proud to be involved.
"We got the five points to move on to face Uruguay, which we knew would be a tough challenge after seeing their display against France."
A poor first half performance saw Italy 17-7 down to Uruguay at the break, but was turned around as they scored 31 unanswered points after the interval, Lamb replacing Niccolo Cannone early in that second half.
"If we can take anything from that, it's the grit and determination we showed in the second half.
"It was a really positive outcome, to have been losing at half time and for the team to work together to get the result.
"We'll take it as a positive moving forward, especially as it's a new, young group of players, and with the two wins before the World Cup and now these two, it's great for building confidence and momentum in our performances."
That momentum will now be put to the test, as Italy face New Zealand, a side they have never beaten in 15 meetings.
"We're well aware of the challenge ahead, the All Blacks are what they are, that iconic black jersey, a team of high performers who work very well together as a collective."
Italy have never reached the knockout stages at the World Cup. With his family now coming to France to watch the next two games, Dino Lamb will proudly head into battle.
"I'm excited for it! And we'll take confidence from our last couple of performances. We've put ourselves in the best possible position to create history for Italian rugby."
Italy take on New Zealand on Friday in Lyon and their final Pool A game with France is on October 6.