Wash the potatoes well. Bring them to a boil in a large pot of water, and remove them when they are tender enough for a fork to break through them easily (about 15-20 minutes).
Using a mortar and pestle, pound and crush the garlic and a little salt to a pulp. Peel the first potato- they should all be hot- and pound it together with the garlic, drizzling in olive oil and lemon juice, until the potato is creamy. Repeat with remaining potatoes, olive oil, and lemon juice. Adjust seasoning with salt and additional olive oil and lemon juice if necessary. Serve immediately.