Liquid phase crystallized silicon thin-film solar cells on glass provide efficiencies up to 14.2 %. While open-circuit voltage and fill factor are already comparable to wafer-based devices, short-circuit current density is reduced due to incomplete light absorption. This paper analyzes the losses of current device designs in experiment and one-dimensional simulations, revealing the low absorber thickness of 15-20 μm as well as the planar glass-silicon interface as the main cause of non-absorption. Interface textures, in particular a sinusoidal texture and a smooth anti-reflective three-dimensional (SMART) texture, are discussed concerning their potential to mitigate these losses, allowing to reduce losses at the glass-silicon interface by at least 40% relative. Taking the electronic interface quality into account, the SMART texture is identified as the most promising texture for light management in liquid phase crystallized silicon thin-film solar cells on glass.