  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 107.6 days via radial velocity
monitoring (Udry et al. 2019). The two inner planets (b and c) were recently
found to transit (Kane et al. 2020), 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 $2.56\pm0.09$ $R_{\oplus}$ and $8.82\pm0.94$ $M_{\oplus}$, respectively.
With its bright Sun-like star, long period, and mild irradiation ($\sim$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 likely 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.
