Debiasing techniques such as SentDebias aim to reduce bias in large language models (LLMs). Previous studies have evaluated their cross-lingual transferability by directly applying these methods to LLM representations, revealing their limited effectiveness across languages. In this work, we therefore propose to perform debiasing in a joint latent space rather than directly on LLM representations. We construct a well-aligned cross-lingual latent space using an autoencoder trained on parallel TED talk scripts. Our experiments with Aya-expanse and two debiasing techniques across four languages (English, French, German, Dutch) demonstrate that a) autoencoders effectively construct a well-aligned cross-lingual latent space, and b) applying debiasing techniques in the learned cross-lingual latent space significantly improves both the overall debiasing performance and cross-lingual transferability.