The key difference between Lucite and Acrylic is that the Lucite is the tradename for polymethyl methacrylate whereas Acrylic is the general chemical name of polymethyl methacrylate.
Acrylate polymers are what we call plastics. They have noted transparency, resistance to breakage, elasticity, etc. Therefore, in general, we call them acrylic polymers. The most common type among these polymers is polymethyl methacrylate (PMMA). Therefore, we call this polymer as “acrylic” or by its trade name “Lucite”.