Exoplanets transiting bright nearby stars are key objects for advancing our knowledge of planetary formation and evolution. The wealth of photons from the host star gives detailed access to the atmospheric, interior and orbital properties of the planetary companions. nu^2^ Lupi (HD 136352) is a naked-eye (V=5.78) Sun-like star that was discovered to host three low-mass planets with orbital periods of 11.6, 27.6 and 107.6d via radial-velocity monitoring. The two inner planets (b and c) were recently found to transit2, prompting a photometric follow-up by the brand new Characterising Exoplanets Satellite (CHEOPS). Here, we report that the outer planet d is also transiting, and measure its radius and mass to be 2.56+/-0.09R_{Earth}_ and 8.82+/-0.94M_{Earth}_, respectively. With its bright Sun-like star, long period and mild irradiation (~5.7 times the irradiation of Earth), nu^2^ Lupi d unlocks a completely new region in the parameter space of exoplanets amenable to detailed characterization. We refine the properties of all three planets: planet b probably has a rocky mostly dry composition, while planets c and d seem to have retained small hydrogen-helium envelopes and a possibly large water fraction. This diversity of planetary compositions makes the nu^2^ Lupi system an excellent laboratory for testing formation and evolution models of low-mass planets.