The authority, which is under No Overall Control, says demand for services such as housing homeless families has gone up dramatically.
Councillors will host a public meeting on the situation on October the 15th.
They says in the meantime, they are going to be proactive in rooting out genuine waste by taking services in-house and “investing to save.”
Cllr Zvikomborero Chihoro, Lambeth Council’s Cabinet Member for Finance and Community Wealth Building, said: “This is an incredibly serious situation. The funding cuts being imposed will harm our communities. Decisions made in Westminster are putting valuable local services in crisis and we are not willing to accept that.
“We are also going to be creative and pro-active to protect front-line service – rooting out genuine waste, taking services in house, opening the books, and investing to save.
“Lambeth Council provides hundreds of services, from caring for older people and looking after children with special needs, to running dozens of parks, libraries and children’s centres.
“Many of our services are unseen, supporting the most vulnerable in our communities, creating social networks and tackling equality. We believe these are service worth fighting for and are proud to deliver them.”
