The 23-year-old centre limped out of their European Rugby Champions Cup clash with Ulster at the weekend with a groin injury and was not named in the 33-man England squad announced earlier on Wednesday.
The most important person in all of this is Manu and we have to make sure we get his rehabilitation right
In his place is Bath centre Jonathan Joseph, while Saracens centre Brad Barritt and Northampton Saints’ Luther Burrell were also named and the trio are set to contest the 13 jersey for the contests against New Zealand, South Africa, Samoa, and Australia.
“The reason we brought Jonathan Joseph into the camp is that Manu won’t be fit for the start of the series, but we have not shut the door,” Lancaster said.
“It could take six weeks but we’ll never say never. It’s a joint management programme between us and Leicester and between us we have to get it right.
“The most important person in all of this is Manu and we have to make sure we get his rehabilitation right and get him some game time. There’s no definitive timeline. It’s not that sort of injury.”
Despite the inclusion of wingers Marland Yarde and Jack Nowell, Bath wing Semesa Rokoduguni could make his senior international debut against the All Blacks on Saturday 8 November.
“We’re keen to get working with him because he’s been outstanding for Bath,” Lancaster said of the former soldier with the Royal Scots Dragoon Guards.
“When you lose someone like Manu, Roko comes into the equation because of his impact in collisions, his ability to beat defenders and carry the ball over the gainline. He’s a finisher as well.”
Lancaster has also insisted there is no issue in the midfield for the four matches, despite the loss of Tuilagi and Gloucester captain Billy Twelvetrees out of form.
“I wouldn’t say the centres are an area of concern,” he said. “Brad Barritt and Kyle Eastmond have both been outstanding and you have Luther Burrell and Billy Twelvetrees there as well. There’s plenty of competition.
“Then there is Jonathan Joseph, who is perhaps the form centre of all of them. It’s about balance – you want a balance of pace, power and footballing ability.
“We will see them head-to-head, and we will make our decisions on the combinations.”
MORE: The latest football news
MORE: The latest tennis news
BIOGRAPHY: Ethan Hazard
BIOGRAPHY: Daniel Sturridge