Midfielder Lawrence has reached a compromise agreement with Pompey's administrators, paving the way for former owner Balram Chainrai's company Portpin to buy back the stricken south-coast club.
Administrator Trevor Birch had set a deadline of Friday for every senior player to be off the wage bill, otherwise he would have to close Pompey down.
"We have negotiated a compromise agreement with Liam Lawrence, who will leave the club when the paperwork is finalised later today," read a statement on Pompey's website.
"I'd like to thank Liam for his support and all of the other players for putting the club's interest ahead of their own. They have all had to make very difficult decisions and been placed in an impossible position which wasn't of their making."
Birch added: "This means that we have now successfully completed agreements with all of the first-team squad and met the major condition of the offer from Portpin, which formed the basis for the CVA proposal."
Portsmouth will now be able to start the npower League One season next weekend, albeit with another 10-point deduction following their latest spell in administration.
Before that their competitive campaign begins with a Capital One Cup first-round trip to Plymouth on Tuesday.
Manager Michael Appleton will be hoping the takeover is completed by then so he can recruit some players, having been working with a mixture of youngsters and trialists during pre-season.
Chainrai still has opposition in his bid to buy back the club, with the Pompey Supporters' Trust also in the running and boosted by a £1.45million loan from the local council.
Birch said: "We will now aim to finalise our discussions with Portpin with a view to completing the sale of the club as soon as possible.
"The intention is to push this through early next week in order to ensure that player recruitment can begin as quickly as possible for the start of the new season.
"The offer from the Pompey Supporters' Trust remains a fall-back position and we are pleased to note that the council has agreed to provide a loan facility to support the Trust bid."