The council is due to accept a confidential report from The Barony Group which says that the authority's housing benefit service is "failing" and that the staff and systems involved should be brought back in-house.
Computer Weekly has also learned that in correspondence Lambeth has made an £18m legal claim against Capita, which is one of the largest government IT suppliers. The supplier is understood to have made a claim of its own.
The Barony report says that Capita had been asked to indicate what it might cost to bring the service to a "satisfactory level" within 18 months.
The supplier proposed charging an extra £20m, on top of fees already due to Capita under the original £48m contract.
The Barony Group recommends bringing the service in-house rather than paying the "extraordinarily high price" suggested by Capita.
This will mean cancelling the seven-year outsourcing deal three years before it is due to expire in 2004, and bringing the systems and staff back in-house.
But Lambeth's council tax payers still face paying millions of pounds in extra costs. The report warns that the council should set aside a "very large transitional budget" to pay for the service's return.
This budget would include the costs of hiring key managers from Capita, and the hand-over of IT systems and office equipment.
The extra transitional costs will be on top of £3.5m that Capita has already been paid in the past year beyond the original contract price.
The Barony Group's report paints a picture of a council facing a privatisation nightmare.
There are many uncertainties about whether the council will be able, in the short term, to secure the staff and equipment needed to run a satisfactory service.
Meanwhile the failing service is hitting the public. Landlords have threatened to evict tenants who cannot pay the rent because housing benefits have not been paid.
Lambeth says it has a backlog of 30,000 claims, although this is down from about 100,000 when the Capita contract began in 1997.
Capita staff believe that the initial bid may have been too low, partly because the council had underestimated the number of highly-paid agency staff who were working in the housing benefit department. They also suggest that unforeseen extra Y2K work caused delays.
The council declined to comment.
A Capita spokeswoman said, "We are hoping to reach an amicable and professional agreement over what areas the council would wish Capita to continue to support."
Several councils have run into problems with housing benefit systems. Hackney council cancelled its contract with ITnet, leaving the authority without IT systems to administer the benefit.