Have ready a bowl of ice water. Boil a large pot of water over high heat, and add a generous amount of salt. While waiting for the water to boil, cut off the bottoms of the rapini stems, remove any large, bruised leaves, and wash well. Blanch the broccolini for one minute, until the leaves have softened but the stems are still nice and firm. Remove the broccolini using tongs or a spider, and place in the bowl of ice water to stop the cooking process and help keep its vibrant green colour.
Heat the olive oil in a large sauté pan over medium heat. Add the garlic and chili flakes. Add the whole pieces of broccolini and the sun-dried tomatoes, and generous pinches of salt and freshly ground pepper. Increase the heat to medium-high heat and cook about two minutes.
Transfer the mixture to a large serving platter. Right before serving, crumble the goat cheese over the top. Add the lemon juice.