  The CP-violating interaction of the nuclear magnetic quadrupole moment (MQM)
of the $^{175}$Lu nucleus with electrons in the molecular cation LuOH$^+$ is
studied. The resulting effect is expressed in terms of CP-odd parameters, such
as quantum chromodynamics angle $\bar{\theta}$, quark electric dipole moment
(EDM) and chromo-EDM. For this we have performed a calculation of the nuclear
MQM as well as the molecular constant that characterises the interaction of
this MQM of $^{175}$Lu with electrons. Additionally, we predict the hyperfine
structure constants for the ground electronic state of LuOH$^+$. We conclude
that LuOH$^+$ is a promising system to measure the nuclear MQM.
