Lord Janner died at the end of last year, shortly after a judge had ruled that the he was not fit to stand trial for alleged child sex offences.
But a leading lawyer has told the BBC he sees "a danger" that the inquiry into Lord Janner's case may contravene the principles of a fair trial.
As part of her wider inquiry, Dame Lowell, who served as a judge in her native New Zealand, will investigate the way public bodies handled child sex abuse claims.
She will be holding further preliminary hearings this month into allegations of child sexual abuse involving the Anglican Church, Lambeth Council and a number of institutions in Rochdale.
The inquiry will consider the prevalence of abuse and the adequacy of child protection policies.
At this stage, though, it will not hear from witnesses.
Instead, Dame Lowell has designated 17 complainants in the case as core participants, giving them access to relevant evidence and the opportunity to make opening and closing statements.
Core participants will be able to ask for particular questions to be put to witnesses by the inquiry panel but they will not be allowed to question the witnesses directly.
In setting out the scope of the investigation, Dame Lowell says she will consider whether or not the allegations against Lord Janner are "well-founded".
It is only if particular allegations meet this test that she will go on to consider whether the various authorities concerned had failed in their responsibilities.
This suggests that she intends to hold what amounts to a trial without a defendant.
Last April, her team said: "If the evidence permits findings of fact to be reached concerning the allegations against Lord Janner, the inquiry will record and publish these findings."
If Lord Janner's criminal trial had gone ahead, prosecutors would have had to prove the allegations against him beyond reasonable doubt.
However, it is thought that the Goddard inquiry will regard the allegations as well-founded if they can be proved on the balance of probabilities - the lesser standard of proof required in civil claims.
Another question for the inquiry is whether witnesses who claim they were abused by Lord Janner should be cross-examined, as they would have been at a criminal trial.
Unless lawyers for the various core participants are willing to challenge the evidence given by individual witnesses, Dame Lowell may have to consider appointing independent lawyers for the purpose.
That's because the inquiry's findings may have a bearing on civil claims being made against the estate of Lord Janner and against the various public bodies that are accused of failing in their safeguarding duties.
Prof Sir Ian Kennedy QC, who chaired the public inquiry into child deaths at Bristol Royal Infirmary which reported in 2001, said there was a danger that Lord Janner's case would become something like a trial.
In an interview for BBC Radio 4's Law in Action he said: "The difficulty is that it can't really be a trial, as we would recognise it, because the person who is centre stage is no longer there.
"And that will pose very difficult questions about tackling the veracity or otherwise of witnesses."
Sir Ian asked whether anyone would represent Lord Janner's interests at the inquiry.
He concluded: "There is a danger, if you convert it into a trial, of it contravening some of the principles which we normally associate with a trial."
Lord Janner's family have always denied the allegations against him.
For more on this story listen to Law in Action.
Dame Lowell Goddard's independent inquiry into child sexual abuse has begun hearing legal submissions about the scope of her investigations into the late Labour peer Lord Janner.