  The LuOH$^+$ cation is a promising system to search for manifestations of
time reversal and spatial parity violation effects. Such effects in LuOH$^+$
induced by the electron electric dipole moment $e$EDM and the
scalar-pseudoscalar interaction of the nucleus with electrons, characterized by
$k_s$ constant, in LuOH$^+$ are studied. The enhancement factors, polarization
in the external electric field, hyperfine interaction, rovibrational structure
are calculated. The study is required for the experiment preparation and
extraction of the eEDM and ks values from experimental data.
