Lucy is occasionally seen using her aluminum double boiler, but perhaps most famously when she heats up a potion to use on Ricky’s hair in the hilarious scene from which the above captures are taken. 
Lucy’s double boiler has a distinctive shape that widens at the base which helps narrow down the possible makers when searching for a vintage one like it. A good match is this vintage Comet double boiler seen on ebay today.
A double boiler is really two saucepans – a smaller one fits above the base pan below. The base saucepan is used to hold simmering hot water which should not touch the bottom of the top pan so that the steam creates a gentle heat without burning. It is used when you don’t want direct heat under the item you are cooking, such as when making certain custards or sauces, melting chocolate etc.