Peel cucumber and dice. Dice the onion. Add the cucumber, onion, and garlic to a food processor. Process until the vegetables are minced.
Add the arugula and mint to the food processor along with the olive oil and the flesh from the avocado. Purée until smooth.
Add the water, one tablespoon of lemon juice, and salt. Purée until smooth again. Taste the soup and adjust the salt or lemon juice if desired.
Serve immediately or chill in the fridge until ready to eat. Garnish with diced tomato.