In a 12-1/2 hour session in US federal court, Lloyd's attorneys sought approval for a plan designed to keep it solvent after multibillion-dollar losses from insurance claims.
Lawyers for the investors said the plaintiffs needed more information before agreeing to the complex plan to settle nearly $5 billion in insurance losses.
US District Judge Robert Payne said he would rule on the matter by Thursday afternoon. No hearings are scheduled for Wednesday.
The hearing is the latest in a series on Lloyd's recovery plan. The programme has been approved in Britain and in other US federal courts, but 93 of about 3,000 US investors filed suit in the Virginia court to block it.
Lloyd's needs to pass the rescue proposal by Aug. 28. A court order blocking it would upset the recovery of a market reeling from $12.4 billion in losses from asbestos, pollution and disaster claims between 1988 and 1992.
"If the ... plan is not complete, Lloyd's cannot pass its solvency test," Chief Executive Ronald Sandler told the court.
He testified for six hours on Monday and Tuesday. Under the rescue proposal, Lloyd's would reinsure liabilities, including pollution and asbestos-related claims, in the United States through a new company called Equitas. But investors found the offer short on details.
They said Lloyd's had not yet provided adequate pro forma financial statements for Equitas or solid information on such points such as who will operate it, what its costs will be or how its funds and proceeds will be used.
"We are here to try to make sure we get that information," said Steve Clay, one of the lawyers for the plaintiffs. Lloyd's attorney Michael Rauch told Payne it would take months for the information to be sent to investors.
Lloyd's said it was willing to allow investors to sue in Britain if fraud was found in its restructuring.
Lloyd's executives expect the liabilities to be wiped out in 30 years and any money left over would go to charities. The names of the charities are to be put before Payne before he rules.
Sandler said Equitas would have a set of trustees to run it and one Lloyd's director would be among them.