With a stand mixer (or hand mixer) and its wire whip, beat eggs and sugar for about 3-4 minutes until fluffy.
Add yogurt, oil and vanilla extract. Stir to incorporate.
In another bowl, sift flour, baking powder and salt, then add lemon zest. Add one tablespoon of this mixture to the raspberries to "coat" them so they don't sink when the loaf cake is baking.
Add the flour to the wet ingredients and mix just until combined.
Add raspberries and stir gently.
Grease a loaf pan and line with parchment paper (or flour), add the batter and bake for 40-45 minutes
While the cake is baking, prepare the sryup: add 2 tablespoons of lemon juice and 2 tablespoons of sugar into a small pan, let melt and simmer for one minute.
When the loaf cake is ready, let it cool down a little bit then punch some holes all over it and pour or brush the syrup on top.