We apply sparse, fast and exible adaptive lapped orthogonal transforms to underdetermined audio source separation using the time-frequency masking framework. This normally requires the sources to overlap as little as possible in the time-frequency plane. In this work, we apply our adaptive transform schemes to the semi-blind case, in which the mixing system is already known, but the sources are unknown. By assuming that exactly two sources are active at each time-frequency index, we determine both the adaptive transforms and the estimated source coefficients using l1 norm minimisation. We show average performance of 12-13 dB SDR on speech and music mixtures, and show that the adaptive transform scheme offers improvements in the order of several tenths of a dB over transforms with constant block length. Comparison with previously studied upper bounds suggests that the potential for future improvements is significant.