Peel and coarsely grate the sweet potatoes. Chop the pineapple in the universal chopper. Wash lemon hot, grate dry and grate peel thinly.
Mix the sweet potatoes, pineapple, lemon peel, oil, 400 g yoghurt and agave syrup with the whisk of the hand mixer. Mix flour, baking powder and baking soda. Stir the flour mixture into the sweet potato mixture.
Put the dough into an oiled box form (1.2 litres capacity; length at the bottom: 23 cm; length at the top: 26 cm) and smooth it down. Bake in a preheated oven (electric cooker: 175 °C/ convection oven: 150 °C/ gas: see manufacturer) for 55-65 minutes (stick test).
Take the cake out of the oven and let it cool down on a cake rack for about 2 hours. Just before serving, pour the remaining yoghurt onto the cake and drizzle a spoonful of syrup over it.