Lucy Letby, a former neonatal nurse who was convicted of the murder of seven babies and the attempted murder of seven others, will seek to appeal one of her convictions in a London court on Thursday.

The appeal hearing comes amid renewed scrutiny of Ms. Letby’s case, as a growing number of statisticians and medical experts have questioned the reliability of the evidence used by the prosecution.

Ms. Letby, 34, who has always maintained her innocence, is serving 15 life sentences after she was found guilty of harming babies at the Countess of Chester Hospital in northern England between 2015 and 2016.

During her trial, the prosecution told the jury that she had harmed babies through a macabre range of attacks: injecting them with air, overfeeding them with milk, infusing air into their gastrointestinal tracts and poisoning them with insulin.

Thursday’s hearing will focus on one of the attempted murder convictions, for a child known as Baby K, and the judges will then deliver a decision at a later date over whether a full appeal will be heard.

Ms. Letby has already been denied appeals in the other seven murder and six attempted murder cases for which she is serving life sentences.

Last month she appointed a new defense lawyer, Mark McDonald, who plans to apply to Britain’s Criminal Cases Review Commission, the official body responsible for investigating alleged miscarriages of justice in the country, and the one remaining way for her other criminal convictions to be revisited.

“I can tell you now, if I was innocent and in prison, I’d rather be in the U.S. than the U.K.,” said Mr. McDonald. “It is so difficult to overturn a conviction in this country, it is almost impossible.”

Mr. McDonald said that in his application to the C.C.R.C. he would focus on the reliability of the evidence presented by the prosecution, rather than claiming that Ms. Letby’s original defense was insufficient, and plans to submit the case within weeks.