“When I think about my husband, who I thought he was, compared to this man, this man seems like a complete stranger to me,” Lucy told the BBC.
“It makes me sick to think that he will be near my child at all. So I really don’t want to put my baby in a room with a stranger, supervised or unsupervised.
“As a mother, all I want to do is protect my child, and I won’t do that if I let him.” [them] in a room with a stranger.”
Lucy said she understood her call for the law to be changed was a “huge” demand, but it was aimed at protecting children and families.
Earlier this year, Finance Minister John O’Dowd committed to changing family laws to automatically remove parental responsibility from anyone convicted of murdering someone with whom they shared a child.
Lucy said she believed this should apply to anyone on the sex offenders register, including her ex-husband.
She said she believes the move could also help deter people from offending.
A Treasury spokesman confirmed O’Dowd intends to develop legislation that will provide “greater protection for children and families.”
In England and Wales, Jade’s Law automatically suspends parents’ liability for the murder or culpable manslaughter of a partner or ex-partner with whom they share children.
It is named after Jade Ward, who was 27 when she was killed by ex-partner Russell Marsh in 2021.
However, Jade’s Law does not apply to Northern Ireland.
A Treasury spokesman said a consultation would be launched this autumn to set out proposals for reform in murder cases and “whether comparable protection should be extended to other forms of serious offences”.