The plea is part of a deal made with the Crown to have the charges reduced from second-degree murder in the deaths of Carolyn Sinclair, 25, and Lorna Blacksmith, 18.
The deal calls for two 10-year sentences for a total of 20 years in jail. The judge has not yet ruled on accepting the deal.
Lamb, 54, was charged in June 2012 with three counts of second-degree murder in connection with the deaths of Sinclair, Blacksmith, and another woman, Tanya Jane Nepinak, 31.
He has been in custody since then.
On Thursday, Lamb waived his right to a trial and made his plea, prompting family members of Sinclair and Blacksmith to begin crying in court.
Sinclair's body was found in March 2012 near a dumpster behind an apartment complex in the 700 block of Notre Dame Avenue, between Toronto and Victor streets, in Winnipeg's West End.
Court heard on Thursday that Lamb and Sinclair had been smoking crack cocaine in Lamb's bathroom, when Lamb hit her with an axe handle on left side of her head.
Lamb then smoked the rest of the crack and left Sinclair's body in the bathroom for several days before placing her in a bag and dumping her, court was told.
Blacksmith's body was found in the backyard of a home in the 700 block of Simcoe Street, also in the city's West End, in June 2012.
Court was told Thursday Blacksmith was strangled with a TV cord. Lamb then went to buy drugs and dumped her body later that day.
The Crown prosecutor told court the investigation was challenging because there were no witnesses and little forensic evidence, which is why the charge was reduced to manslaughter. The conviction is based solely on Lamb's statement.
The Crown said public safety was the primary concern in making the deal with Lamb.
Lamb’s lawyer, Martin Glazer, said the judge should consider that his client confessed in June 2012 while in custody on unrelated matter, then helped police fill in the blanks about those homicides.
Police had no idea Lamb was involved until he came forward.
“How many people in his shoes would do that" especially given lack of evidence and unlikelihood of a conviction, Glazer said.
Nepinak's body has never been found but police have declared her as a homicide victim.
Police have said they believe Nepinak's body was placed in a garbage bin in the city's West End and that the bin was emptied in the Brady Road landfill. But a week-long search of the area in October 2012 turned up no evidence.
Her death remains an open case.
Lamb, who is originally from Ontario, has an extensive criminal record extending across four provinces.
Since 1979, he has had 109 convictions in Ontario, Alberta, B.C. and Manitoba. In the latter, Lamb has 45 convictions since 2002 for everything from robbery to forgery, fraud, and uttering threats.
Most recently he was charged with sexual assault in May 2012 and June 2012.
It was when Lamb was picked up on June 21, that police learned of his alleged connection to the three homicides.