The troubled TV presenter who is in recovery from drink and drug addictions is claimed to have told her to take anything but the chocolate Labrador has they argue about their multi-million pound divorce settlement.
Lisa's pal told the Daily Mail: "They are fighting about money and about a non-disclosure agreement which Ant’s team want her to sign and she is refusing.
"But most of all, it is about the dog. They cannot agree.
"Both of them will be heartbroken if they lose Hurley. He has said she can have anything she wants — except for Hurley."
The estranged couple's 11-year marriage came to an end four days ago when a judge issued a decree nisi during a hearing which lasted just 30 seconds.
The former teenage sweethearts, who announced their split in January with an emotional statement, struggled to start a family during their relationship.
Lisa refers to Hurley as her "baby" and her "baby boy" since he became part of the family in 2013.
Now they are thrashing out a settlement over Ant's £62million fortune – and who should look after Hurley full-time.
The Sun revealed they are clashing over Lisa's refusal to sign a non-disclosure agreement to stop her talking about Ant's behaviour.
Strictly make-up artist Lisa won't agree to be gagged as part of any deal, telling pals: “I will not be silenced."
Ant was fined £86,000 in March after a drink drive smash after battling prescription drug addiction.
He announced he was taking a break from his TV commitments, including Saturday Night Takeaway and I'm a Celebrity to focus on his recovery.
Ant is now happily loved up with his former PA Anne-Marie Corbett who he went official with over the summer.
Meanwhile Lisa has until now found it difficult to move on from her estranged husband.
On Thursday she hinted she is moving on from a "hideous year" by 'liking' a series of tweets about how she's held herself together.
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