Slice the radishes into thin slices as best you can, using a sharp knife. Put them into a bowl.
Put the lime juice, sugar, red onion, olive oil and dill into a smaller bowl. Stir together, then add to the radishes and mix gently. This only needs 10 minutes to infuse.
Meanwhile, toast the sourdough.
Mash the avocado with the reserved 2 tablespoons of lime juice, to prevent any browning. Spread the toast with the avocado and add a sprinkling of black pepper.
Drain the radishes through a colander to remove any excess lime juice, and place slices of radish and onion on top of the avocado.
