Grate 2 teaspoons zest from 1 lemon. Trim ends of both lemons, then stand lemons on a cut side and cut peel, including white pith, from lemons with a sharp paring knife (discard peel). Cut segments free from membranes, then cut segments crosswise into 1/4-inch pieces. Toss lemon segments gently with sugar in a bowl and stir in 2 tablespoons oil. Let stand at room temperature 10 minutes for flavors to develop.