In a bowl, combine the thinly sliced red onion and salt. Let it sit for about 10 minutes to soften the onion and draw out excess moisture.
Rinse the onions under cold water to remove excess salt, then drain well.
In a large mixing bowl, whisk together the olive oil, lemon juice, sumac, and black pepper.
Add the drained onions to the bowl and toss to coat them in the dressing.
Gently fold in the chopped parsley and cherry tomatoes, if using.
Let the salad sit for at least 15 minutes before serving to allow the flavors to meld.