I just found this recipe but didn’t make a note of the source. So sorry not to be giving it proper attribution.
Ingredients:
1 pound cucumber(s), peeled or unpeeled, cut into large chunks, plus a few extra thin cucumber slices for garnish 1 cup lemon juice (from about 7 to 8 lemons, although juiciness will vary) 2 cups cold water 1/3 cup granulated sugar
Preparation:
Run cucumber through a blender or food processor until pureed, then run it for a full extra minute to ensure that it’s as processed as possible. Set a fine-mesh strainer or a regular strainer lined with a couple layers of cheesecloth or a coffee filter over a pitcher and pour cucumber puree through it, stirring to help it move along faster. Discard solids. In the pitcher, you should have about 1 cup cucumber juice. (You could also just use a juicer.)
Add lemon juice and sugar to it, then water. Give it a good stir or shake, and let it sit in the fridge (to get it started chilling) for 15 minutes, after which a couple more stirs or shakes should leave the sugar fully dissolved. Taste lemonade, adding more sugar or water if desired. Serve chilled over ice, with or without a splash of seltzer on top. You can fancy up the glass with a garnish of cucumber slice, if desired.