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:
Fermax yeast nutrient is made up of diammonium phosphate, dipotassium phosphate, magnesium sulfate and autolyzed yeast.
Most yeast nutrients have yeast hulls, and DAP in them. You can also just boil some older yeast too.
You can find it at any homebrew store or online homebrew store.