In a 2- to 3-quart pan over medium-high heat, frequently stir oil and onion until onion is limp, 7 to 9 minutes. Add rice and stir 1 to 2 minutes more.
Add wine, 1/4 cup water, tomato sauce, mint, currants, garlic, Italian seasoning, and pepper. Mix and bring to a boil. Cover and simmer over low heat, stirring occasionally, until rice is almost tender to bite, 12 to 15 minutes. Uncover and let cool at least 20 minutes.
Meanwhile, rinse grape leaves, drain, and pat dry. Line the bottom of a 9- by 13-inch baking dish with 5 or 6 leaves. Reserve 5 or 6 additional leaves.
With scissors, trim stems from remaining leaves. To fill each leaf, place underside of leaf up with stem end toward you. Shape 1 tablespoon seasoned rice filling into a 2-inch log across stem end of leaf. Fold leaf sides over filling and roll snugly. Fit filled leaves, seams down, in a single layer in leaf-lined dish. Cover with reserved leaves. Mix 1 cup water and lemon juice. Pour over rolls. Seal dish with foil.
Bake in a 350° oven until liquid is absorbed, 30 to 45 minutes. Serve warm or cool.
Nutritional analysis per roll.