Remove any blemishes from rhubarb stalks and pull off as many strings as you can, celery-style, as these will jam the juicer. Juice at high speed. If the machine balks, turn it off and clean out the blade (this often happens when I do ginger, too). Do not force it to continue if it sounds abnormal... just clean it out!
Pour off everything except foam head into a coffee filter/cheesecloth/etc; once it passes through, the juice will be a gorgeous deep, translucent, fuschia color. Don't drink this straight! I tried a little just to see and it is so incredibly unpalatable even in tiny volume. Plus it is too high in oxalic acid to drink on its own. (This juice will last about two days in the fridge.)
Remove peel and pith from lemons and juice them in the juicer. Discard foam. (Reserve peels for another use, such as candying, if you like.)
If you've just made the simple syrup (one part sugar to one part water, brought to a boil and left for a few minutes), allow it to cool at least to room temp.
Shake with ice the following (or mix in pitcher with ice):
1 part rhubarb juice
2 parts lemon juice
3 parts simple syrup
These are the proportions given in the recipe, so you can mix it all at once or keep ingredients separate and prepare individually at whatever pace you like.
Note: This comes out very full-flavored, which is how I like it; just enough water from the ice. If you prefer a mellower taste, dilute as you wish. Cheers!