I am trying to prepare alcoholic lemonade using: lemons, water, dextrose, lactose, and champagne yeast. I read that it is a good idea to add yeast nutrient but I have no idea what it is or where to find it. Any idea from somebody about it being important for this type of fermentation?
Yeast needs a few things to survive besides just sugar. Things like nitrogen, lipids, etc. When you make an all-grain batch of beer, you get a lot of these things from the mash. But when you use "refined" sugars, like table sugar, the yeast needs a little help. You can buy nutrients at a homebrew shop.
Take a look at this page from "How to Brew" by John Palmer, with more details, and a few commercially available examples: