Lucite is a variant of plexiglass/acrylic. Exceptionally clear, clearer than glass even and one of the clearest known solids, which makes it a great looking substance to use on waterblocks, especially when heat-treated which gives it that lovely glossy appearance. Unfortunately it isn't that strong, and is prone to cracking if "shocked" or overtly stressed.
Polycarbonate is a different style of plastic altogether and is much tougher and more durable, so long as you don't go for the glass-based varieties which have a percentage of glass in them (much like a metal alloy). Non-glass based polycarbonate is around 30x stronger/tougher than the acrylic based plastics. Polycarbonate is less transparant though. Perhaps about 1/3 as transparant as glass which can make it slightly murky for thickness greater than 10mm or so.