Petty was the subject of a strong offer from Adelaide to return to his home state during the current trade period.
But Lamb emphatically shut down the possibility, declaring the 23-year-old swingman will remain with the Demons.
"100 per cent. That's 100 per cent," Lamb told Trade Radio on Monday.
Petty is contracted to Melbourne until the end of 2025, when he will become a free agent.
"We've had a number of chats with Harrison and we understand Harrison's a real good player," Lamb said.
"That's why Adelaide would like to get him and it's why we're keeping him.
"We'll work to hopefully not having him only for the next two years but an extended period after that."
Petty featured in Melbourne's drought-breaking 2021 premiership as a defender but spent plenty of time in attack this year as the Demons searched for more potency.
He kicked 12 goals in 14 games, including a career-best six in a win over Richmond in round 20.
A week later, he sustained a foot injury that brought an early end to his season.
Melbourne are keen to pair Petty with emerging key forward Jacob van Rooyen next year and beyond.
"We're really excited about that partnership," Lamb said.
"What we saw from it this year was really good and they clicked together well. That's where he'll be playing for us."
The Demons and the Crows remain locked in negotiations over a deal for Shane McAdam.
Melbourne and Adelaide remain locked in negotiations over a deal for Shane McAdam, who has requested a trade to the Demons.
Melbourne have offered the Crows a future second-round draft pick in exchange for the 28-year-old, 50-game forward.
"We think that's a really fair offer and that it gets it done," Lamb said.
Lamb confirmed Jake Melksham will play on with Melbourne in 2024 despite a serious knee injury that will sideline him for most of the season.
Melksham ruptured an anterior cruciate ligament in August, in an incident that initially put the 221-game veteran's playing future in doubt.
"Jake will be at the club next year," Lamb said.
"We are just looking at what his deal looks like. We think he will be back earlier than people think."
Bigoa Nyuon (centre) has joined North Melbourne from Richmond.
North Melbourne have secured Richmond's Bigoa Nyuon, giving up pick 65 for the versatile tall.
Nyuon played one game for the Tigers during his four seasons at Punt Rd.
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