To prepare the lobster, separate the claws from the tail. Crack the claws with a rolling pin and pick out the meat. Remove the shell from the lobster tail, cut the tail in half and discard the intestine. Break off the legs then roll a rolling pin over them to push out any meat. Cut all the meat into bite-sized pieces, cover and put in the fridge.
Put a small saucepan of salted water on to boil. Add the potatoes and simmer for 15 mins until cooked but not broken up. Lift the potatoes out of the water and leave to one side to cool. Add the green beans to the hot water and boil for 3 mins until just cooked. Drain the beans and run under cold water. Put the cooled potatoes and beans in the fridge to chill.
To make the basil dressing, blitz the pine nuts, most of the basil (saving a few leaves to finish), the garlic and red wine vinegar in a small food processor. With the motor running, slowly drizzle in the olive oil. The dressing should be fairly smooth but still have some texture. Season and set aside.
When you are ready to serve, cut the potatoes into 1cm-thick slices, put in a bowl and mix with half the dressing. Arrange the radicchio and green beans on two serving plates, top with the potato slices and finally the chilled lobster. Drizzle over the rest of the dressing, top with the reserved basil leaves and serve.