Place watermelon chunks in a large bowl. Finely chop lemon zest. Add lemon juice and half of zest to bowl with watermelon.
Add mint, oil, and arugula (if using) and toss until watermelon is evenly dressed.
Season lightly to taste with salt and pepper (The cheese will add saltiness, so go light on the salt at this stage.)
Transfer salad to a wide, shallow bowl or a large plate and spread out evenly.
Crumble feta over top. Sprinkle with remaining lemon zest. Drizzle with more olive oil and a few grinds of black pepper. Serve immediately.