Steam or roast beets until tender, then peel once cool.
In a food processor combine beets with remaining ingredients, except oil. Pulse until beets are finely chopped.
With machine running, drizzle in oil until a thick grainy spread is formed (don't over-process into a paste).
Boil noodles until tender, reserving ½ cup of the pasta water and drain well.
Toss noodles and pesto together (may not need all of the pesto), adding just enough of the reserved water until pesto is loosened and a sauce is formed.
Season to taste with salt and pepper, and add more lemon juice if needed to balance out the sweetness from the beets.
Notes
*For low carb - using Shirataki noodles in place of the pasta will be under 9g of net carbs per serving.