Slice the bottom 2cm of the asparagus spears into thin rounds and set aside in a bowl with the lemon juice. Bring a pan of salted water to the boil and boil the potatoes for 10-12 mins until cooked through, adding the asparagus spears for the last 2 mins of cooking. Drain and steam-dry in the colander. Heat the grill to high.
Tip the potatoes onto a baking tray and use a spoon or fish slice to crush them a bit. Add the asparagus to the tray and toss in 1 tbsp of the olive oil, season and grill for 10-15 mins, turning halfway through, until the potatoes are crisp and the asparagus is cooked through and a little charred. Add the lettuce for the final 5 mins until charred. Meanwhile, cook the peas, drain and add these to the lemon juice and asparagus ends. Whisk in the olive oil and season.
Pile the lettuce, asparagus and potatoes onto a large serving dish. Top with chunks of goat’s cheese, the asparagus stalks and peas, drizzling the sauce over the rest of the vegetables as you go. Scatter with dill and lemon zest to serve.