Mr McCue, of H2O Law, said the case would take into account 10 IRA attacks, including the Enniskillen Remembrance Day bombing in 1987, which killed 11.
The Harrods bomb of 1983 which claimed the lives of six people and the Manchester bomb of 1996, in which no-one died, also form part of the case.
Mr McCue said the lawsuits were based on any attack where Semtex allegedly supplied by Libya was used for a bomb or to boost a fertiliser bomb.
He said UK victims of the IRA were able to take action in a US court if they joined a legal action being brought by US citizens.
He added: "This is something we have worked on for two years.
"I thought it was right that the victims have the opportunity for an action to make Libya accountable for sponsoring the IRA."
Mr Parry was awarded the OBE in 2004 for his peace campaigning work, which includes setting up the Tim Parry Johnathan Ball Trust and the £3m Peace Centre in Warrington in 2000.
The H2O law firm is also involved in suing the alleged perpetrators of the 1998 Real IRA Omagh bombing.
The Libyan government has already paid out compensation to victims of the 1988 Lockerbie bombing.
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