His next project will be with the WNO on a production of Die Fledermaus in September.
Lulu is one of two operas to be performed as part of WNO's first themed season.
The WNO has struggled financially in recent years and Domingo had been credited with raising its profile.
Welsh National Opera (WNO) sacked an oboist because his playing risked its world reputation, a tribunal has heard.
He also accused WNO executives of failing to properly investigate the oboist's legitimate complaints of "harassment and bullying".
David Pountney, also the WNO's artistic director, told the Today programme it was purely an "artistic" decision.
"As a lifelong opera lover I'm thrilled to be part of WNO Youth Opera's new production of Paul Bunyan, " said Fry.
Jason French-Williams, defending the WNO, said it was vital that its performers were capable of playing at a very high level.
Placido Domingo's recently vacated post as artistic advisor to the Washington National Opera (WNO) will be filled by the opera director Francesca Zambello.
He described Mr Rizzi, who is no longer WNO musical director and who did not give evidence at the tribunal, as a "vindictive prima donna".
Mr Johnston, who had served with the WNO for 34 years, claimed wrongful dismissal alleging Mr Rizzi bullied and "persistently abused" him in a 16-year vendetta.
The chief executive of the Welsh National Opera (WNO) has defended the decision to put on a Gordon Getty opera after a donation from the Getty family.
Earlier this year, the WNO announced plans to merge with the John F Kennedy Center for the Performing Arts in a move to give it "long-term financial security".
Bieito is the artistic director of the Teatro Romea in Barcelona where he has directed such productions as Carmen and Cosi Fan Tutte for the Welsh National Opera (WNO).
The members of the youth opera not only perform on the same home stage as WNO, but are also mentored by members of the company and other industry professionals.
Some critics raised an eyebrow at the inclusion of an opera by Gordon Getty himself among the new works, but WNO insists he is an accomplished composer that merits performance.
Mr Pountney, who joined WNO in 2011, has worked on operas by Polish artists including Karol Szymanowski's King Roger, Mieczyslaw Weinberg's The Passenger and the forthcoming premiere of Andre Tchaikowsky's The Merchant of Venice.
"The WNO really puts Wales on the cultural map and this programme and the funding that is making it possible will provide Wales with a very welcome boost on the world stage, " he said.
But in June Ms Isherwood expressed concern about an agreement which means while the WNO provides 9% of the performances it is actually using the stage for 30% of the time for its rehearsals.
Mr Johnston had described how he got off to a bad start with Mr Rizzi during the conductor's first stint as WNO musical director in 1994, when he asked him to stop singing at a rehearsal.
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