Ms Lester, 22, was found at her home in Kensington, Liverpool, on Saturday. She had been beaten and repeatedly stabbed. Her daughter, Jade, was discovered close to a reservoir.
John Park, 24, spoke yesterday only to confirm his name during a four- minute hearing before magistrates in Liverpool. An unemployed joiner, of Kensington, Liverpool, he is charged with murdering Ms Lester between 12 and 19 December.
He is also accused of burgling her home in Ling Street before 19 December and stealing property.
Mr Park, wearing a grey sweatshirt and tracksuit bottoms, was remanded into police custody. He will reappear in court later this week. There was no application for bail by the defence solicitor, Gerry Bowen, and reporting restrictions were not lifted.
A nationwide hunt was launched for Jade after her mother's body was found in a recess under stairs in the back dining room of her terraced house on Saturday.
Detective Superintendent Russ Walsh told a press conference yesterday that Ms Lester was a devoted mother: "She was extremely devoted and Jade was a well-cared-for child and well-loved. The family themselves are absolutely devastated."
He said they had still been unable to trace Jade's father: "Unfortunately, Sharon did not divulge the name of the father to her family. We are having great difficulty in tracking the father down.
"If the father is aware of what's happened then we would like him to contact us. It's quite important to the investigation that we trace him."
Mr Walsh said Jade was found by a team of officers including two women constables on waste ground near a reservoir. Her fully clothed body was found in a bin bag, which had been tied with string and left in an overgrown grassy area, where it was hidden from view.
Police heading the investigation said that they had traced two men seen in a white van close to the house in Ling Road and had ruled them out of the inquiry. "They both came forward and have been eliminated in terms of involvement in the offence."
A second man, seen in a yellow van, still has not been traced, he added.
Police are still awaiting the results of a post-mortem examination to discover exactly how Jade died. So far no one has been questioned about her death.