Bring water to a boil in a large pot and add a dash of salt. Add the pasta and cook until almost tender, stirring occasionally, about 7 minutes.
Add the broccolini to the pot and cook 3 minutes more and drain, reserving 1/2 cup of water.
Heat the olive oil over medium-high heat in a large pot. Add the ground lamb. Cook, stirring occasionally, until the lamb is browned and a little crispy, about 10 minutes. Stir in the garlic and the pepper flakes and season with 1 teaspoon of salt. Cook about 1 minute more.
Reduce heat to medium-low and stir the pasta and broccoli into the pot with the lamb. Add the reserved cooking water and continue cooking about 1 to 2 minutes.