Actress Danielle Harold recently joined the BBC soap as Lola, while Murphy will make her on-screen exit as Julie in the coming weeks.
When Billy and Julie's search for their son leads them to discover that he passed away, Billy can't resist trying to locate the granddaughter he never knew he had.
"They're given Dan's things to go through and find out his daughter Lola is in a children's home. Billy's delighted but Julie is so devastated by her son's death she can't get her head around anything new," Murphy told Soaplife.
Admitting that Julie is horrified when faced with meeting Lola because she "hasn't started the grieving process for her son", she added: "And it doesn't help that the first thing Lola says is, 'My dad hated you!'"
However, despite initially being rejected by the teenager, Lola steals Billy's wallet and tracks the pair down to Albert Square.
"Julie's freaked out. Lola reminds her of how she was as a youngster, all the aggression and anger and hatred to the world. Julie doesn't want to revisit the way she was," the actress said. "She doesn't want Lola there. She tells Billy she wants it to be just the two of them. She knows Billy will choose Lola because Billy is a softie and he'll do the right thing by her."
Julie's decision to report Lola for running away from the children's home causes further problems between the pair.
"Billy says he can't bear to look at her. Julie's devastated because she adores Billy," Murphy admitted, explaining that her alter ego only wanted to "teach Lola a lesson".
She teased: "A decision has to be made - Julie or Lola. Julie would normally take Lola on but she can't cope right now. She decides to bow out gracefully and not put up a fight. She's lost her mojo!"
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