Aon and Benfield have been informed they will face action in a bid to force payment of Â£325 million.
Lloyd's says the funds equate to the losses it suffered when six insurers won a legal battle against the London firm.
Costs incurred despite its policy with Aon and Benfield now form the basis of the case.
Lloyd's was left with a Â£500 million bill after losing the case, with the policy providing just Â£152 million.
Now it is planning on retrieving the costs from Aon and Benfield, saying it has informed the duo of its intention, although it has not yet made a formal application to the courts.
The case may not be heard for a further 18 months, although Benfield has said it will "defend any action vigorously".