I make no comment at all on whether the woman in question is right or wrong or whether her dismissal was right or wrong; I have no knowing of the evidence of the case.
But yes, Lord has on multiple occasions actively campaigned for a very partisan political position that is against the rights and equality of women as a sex class, and particularly against their rights to express beliefs in reality, biology and their own sex based words and needs, or simply to express anything at all that is not exactly in keeping with and compliant with his personal and quite extreme TQ+ views. It's as about as inappropriate as asking Posie Parker to take a leading role in deciding a TQ+ access to women's spaces case, or Boris Johnson to lead an ethics committee. It's just plain unhelpful.
He is absolutely not impartial or appropriate to be participating in this, and I would think if the tribunal finds against her she will have legal recourse to overturn the ruling on his background alone.