The best technique for separating glycerol from spent-lye in the soap industry is Distillation under Reduced Pressure, also known as Vacuum Distillation (Option D).

The reason for this is that glycerol has a high boiling point (~$${290^ \circ }$$$$C$$). If we were to use simple or fractional distillation, which involves boiling at standard atmospheric pressure, the high temperature could degrade or decompose the glycerol.

In contrast, vacuum distillation allows the separation to occur at a much lower temperature ( around $${180^ \circ }C$$) by reducing the pressure. This helps to prevent degradation of the glycerol, making it a better method for this particular separation. Steam distillation isn't suitable here, as it's typically used for temperature-sensitive, volatile substances, which isn't the case for glycerol.