Amid rampant speculation about his future, Oliver met with Melbourne ahead of the trade period.
Oliver then attended their club best-and-fairest awards function earlier this month, where president Brad Green made it clear the midfielder would be in their round-one team.
There remained some murmurs about clubs having interest in Oliver, but he is still at the club.
"Simon (coach Simon Goodwin) has been in constant contact with him and Clayton fully understands the situation. He'll be back at training and ready to go," Lamb said at Wednesday night's end of the trade period.
A journalist then pressed Lamb on Oliver being "desperate" to join the Cats.
"I will dispute your term 'desperate' to get to Geelong ... semantics, anyway," Lamb said.
Apart from Oliver, fellow star Christian Petracca is recovering the serious internal injuries that sidelined him for the second half of the season.
View this post on Instagram A post shared by Christian Petracca (@christianpetracca)
Lamb also pointed to their emerging young talent and their fifth and ninth picks in the upcoming national draft.
"One hundred per cent, we will be better," Lamb said.
Despite the significance of Petracca's injuries, Lamb said his recovery is going well.
"If you jump on Trac's social media, he's training like a machine. He's like a big kid, he's that excited," he said.
"The medical advice is that he'll be fine."
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