In a large saucepan, combine the potatoes, bay leaves, and 1 teaspoon of the salt. Add enough water just to cover.
Bring to a simmer, cover and cook, until the potatoes are tender, 10 to 12 minutes. Drain, discard the bay leaves, and transfer to a large bowl.
Add the oil, lemon juice, parsley, and the remaining 1/4 teaspoon salt and toss to coat.