Mr Lambe, who is 25, was last seen leaving a house in Kingsford, an eastern suburb of Sydney, at 12.30pm on Monday.
In a statement issued by the New South Wales police department they said “police and family hold concerns for his welfare due to this behaviour being out of character.”
The local police force believe Mr Lambe is not carrying his mobile phone and does not have access to money.
He was last seen on Middle Street in Kingsford.
Police in the Eastern Beaches Local Area were informed early on Tuesday about the his disappearance, and launched an appeal for information.
The New South Wales police department appealed to anyone with information to contact the Australian Crimestoppers phone line on: 1800 333 000.