In a food processor, combine the kale leaves, basil leaves, walnuts (or pine nuts), and garlic cloves. Pulse until the ingredients are finely chopped.
Add the nutritional yeast and lemon juice to the food processor. Pulse again to incorporate these ingredients.
With the food processor running, slowly drizzle in the olive oil until the mixture becomes smooth and creamy. You may need to scrape down the sides to ensure everything is mixed well.
If the pesto is too thick, gradually add 2 to 4 tablespoons of water until you reach your desired consistency.
Taste the pesto and adjust the seasoning if necessary, adding more lemon juice or salt according to your preference.
Transfer the pesto to a jar or an airtight container and use it immediately, or store it in the fridge for later use.