Cut the crusts off the bread. Soak the slices in cold water in a 20 cm / 8-inch bowl for 5 minutes, then squeeze them hard in your hands or a clean towel until they feel like damp clay.
Grate the onion on the fine side of a box grater. Squeeze the lemons and measure 80 ml juice.
Put the tarama, grated onion and 40 ml of the lemon juice in a 2-liter / 8-cup food processor. Blend for 30 seconds until smooth, then add the squeezed bread in pieces and blend for 1 minute until no lumps of bread remain.
With the motor running, pour in the 200 ml oil in a thin stream over 3 to 4 minutes. Halfway through, add the remaining 40 ml lemon juice. Stop once to scrape down the sides. The dip should turn pale pink and fluffy. If it looks split or greasy, add 1 tbsp cold water and blend for 20 seconds.
Taste the dip. If it's too thick, blend in 1 to 2 tbsp cold water. If it needs more tang, add lemon juice 1 teaspoon at a time. Tarama is salty, so you shouldn't need extra salt.
Spoon the dip into a serving bowl, cover and chill for 30 minutes. Taste again, then serve with warm pita, lemon wedges and olives.