English cricket chiefs are attempting to put legal pressure on the International Cricket Council (ICC) to award them a share of the points, should they boycott their World Cup opener against Zimbabwe.
Lamb says he has a lot of sympathy for the England players
An England and Wales Cricket Board party met the ICC officials on Sunday evening after another day of wrangling.
Death threats and general safety fears looked as though they had convinced Nasser Hussain's side to boycott Thursday's fixture in Harare.
But a decision on the game has been delayed until yet another security review is conducted.
"Specific information regarding the safety and security of the England players and officials came to light earlier today," Tim Lamb, chief executive of the England and Wales Cricket Board, told a news conference on Sunday.
"This information has confirmed the concerns of the ECB that we have had regarding safety and security in Zimbabwe.
"An announcement with regard to whether the England team will travel to Harare to fulfil the fixture has therefore been delayed until the new information has been formally committed to the ICC, and their response has been received.
"This announcement will be made as soon as practically possible. The England team will remain in Cape Town for at least another 24 hours, pending further developments.
A letter was sent to me which did issue an overt threat to the players
ECB chief executive
"A practice session will be held for the England team in Cape Town tomorrow."
Earlier in the day, Lamb told the BBC that a death threat received by the England team had been a "hoax".
Speaking to Radio Five Live, Lamb revealed: "A letter was sent to me which did issue an overt threat to the players.
"I immediately passed it on to the International Cricket Council to share with the relevant security and intelligence sources in South Africa and Zimbabwe, the British High Commission in Harare and Scotland Yard.
"From all the assessments and scrutiny of that letter it is perfectly clear it is a hoax and I think we have been able to persuade the players that indeed is what it is."
The England players were only informed of the existence of the letter this week.
But Lamb defended his decision not to inform the squad of its existence until its validity had been checked out.
England were first warned that they faced possible reprisals if they played in Zimbabwe during the VB Series in Australia.
According to the Sunday Telegraph newspaper, the new threats have come from a group called "The Sons and Daughters of Zimbabwe".
England had asked the International Cricket Council's (ICC) technical committee to move the game from Zimbabwe to South Africa only to have the request denied.
An appeal was then dismissed by a South African constitutional court on Friday.
England's initial request to move the game was made on the grounds of safety, both their own and that of spectators and ordinary Zimbabweans.