The distillation technique most suited for separating glycerol from spent-lye in the soap industry is :

Solution :
Spent-lye and glycerol are separated by distillation under reduced pressure.
Under the reduced pressure the liquid boil at low temperature and the temperature of decomposition will not reach. e.g. glycerol boils at $${290^ \circ }C$$  with decomposition but at reduced pressure it boils at $${180^ \circ }C$$  without decomposition.