Using a medium-sized skillet with a cover, sauté onion in ½ cup of the olive oil until soft. Stir in rice, salt, pepper, and currants. Pour in 1 cup boiling water. Stir, then cover tightly. Cook over low heat until liquid is absorbed, about 20 to 30 minutes. Mix in pine nuts, cinnamon, and allspice. Set aside to cool.
Meanwhile, soak leaves in a bowl of hot water for a few minutes, then rinse each leaf under running water to remove brine. Pat dry and trim stem. Place shiny side down on a smooth work surface with the stem end toward you.
Line the bottom of a heavy skillet or Dutch oven with a layer of leaves (this is a good use for any broken leaves). To fill leaves: Place a generous teaspoonful of the rice mixture in the center of each leaf. Roll from stem-end away from you, folding in sides to make a firm roll.
Lay stuffed grape leaves seam-side down, side by side, on the bed of leaves. Drizzle remaining ¼ cup olive oil over top. Add enough boiling water just to cover. Place a heat-proof plate upside down on top of the rolls to hold them in place. Gently simmer on the stovetop over low heat for about 45 to 60 minutes until leaves are tender.
Drain any remaining liquid. Transfer dolmas to a serving plate and sprinkle with lemon juice. Serve at room temperature.
Note: Pine nuts are generally considered to be a seed, but those with serious nut allergies are often advised to avoid them.