The revised bill to secure compensation for Libya-IRA victims is to receive its first reading in Westminster on Monday.
UUP Peer Lord Empey said his bill was drawn fifth in the ballot out of a total of 46 bills on Thursday, meaning it can proceed at the earliest opportunity – and much faster than he expected.
The second reading of the bill could take place as early as July or September.
His previous bill fell due to the suspension of Parliament for the snap election.
“This is an excellent result and is another good step forward for our campaign,” he said.
“This draw gives the bill a very good chance of proceeding as it has already been through the House of Lords before with full backing.
“I could not be happier.”
The bill would still have to be passed by the House of Commons to become law. This would then authorise the government to tap £10 billion of assets linked to the late Libyan dictator Col Gaddafi which are frozen in the UK. The money could then be used to compensate thousands of Libya-IRA terror victims in the UK on a par with compensation Libya has already paid out to its German, French and US victims.
Col Gaddafi transformed the IRA into a formidable terror group by supplying it with millions of pounds and 120 tonnes of weaponry including large stocks of Semtex during the Troubles.
Lord Empey added: “The fact that we now have a longer Parliamentary session of two years rather than one, in order to facilitate eight huge Brexit bills is also very helpful to us.
“It means it will be much harder for the government to stall it in the commons as they did before.”
The revised bill would allow the government to tap any terror-linked assets frozen in the UK in order to compensate victims, no matter who owns the assets and what terror group they are linked to.
A source said the DUP are pressing the government to accept the recommendations of the Northern Ireland Affairs Committee report in April.
It said the government had badly failed Libya-IRA victims and should resolve the compensation issue urgently.
Lord Empey said he would be “astonished” if the DUP are not doing so.
If the government agrees they will then most likely use his bill as the basis on which to proceed, he said.
In a best case scenario, his bill could become law between now and next Easter, he added.