This following is my personal view formed from my exoerience of handmaking Acrylic bags and repairing Vintage lucite bags and other plastic/Acrylic bags

Lucite bags where first made in the 1940's. It is reported on the internet that the first one was made from a broken nose cone of a damaged aeroplane returning from a mission towards the end of WW11.

 
Wilardy is probably the first manufacturer of Lucite bags. Their business was formed by Charles William Hardy and his son William Hammond Hardy in 1946. Their bags where handmade in their factory and where high end bags and coined them Jewelrey for your arm' other manufactures soon came on board creating their own styles. 
The bags where made from a material called Lucite (tradename )which was manufactured by Dupont. Although other bags where made from different types of plastic including blow moulded bags they are still reffered to today as lucite bags  

I have repaired many original bags but only a couple of Wilardy bags, and in my opinion these where finished the best. 

When watching some of the old films from the 1950's you can see the bags being used as an example Marilyn Munroe in Niagara has a clear lucite bag. 

A lot of the originals have become worn and brittle  over time 60/70 years old. But they are still sort after for collecting or to be used. 

Acrylic was first made as far back as 1928.