Trim the tough ends from the broccolini and asparagus. Discard. Trim the tops and tips from the radishes and slice each radish in half. Add the prepared vegetables to a large saucepan. Cover with boiling water. Simmer over a medium heat for 1-2 minutes until crisp-tender. Drain and immediately rinse under cold water. Drain away any excess liquid.
Add the butter to the saucepan with the drained vegetables. Set over a low/medium heat. Let the butter melt, then start basting it over the vegetables. Keep basting and stirring for 2-3 minutes more to allow the vegetables to cook through in the butter. Add the salt and pepper and stir again.
Remove the vegetables from the pan with a slotted spoon and transfer them to a serving dish. Finely chop the chives. Add the chives to the pan along with the lemon juice. Stir into the butter. Pour the buttery pan juices over the vegetables to serve.