Triatomic cation 175LuOH+, featuring near-degenerate, opposite-parity l-doublets, offers enhanced sensitivity to P - and T -violating interactions. We present ab initio calculations of its electronic structure and rovibrational structure beyond the rigid-ligand approximation by explicitly including OH-ligand deformation together with bending and stretching motions. Potential-energy surfaces are computed at the relativistic coupled cluster level of theory. The nuclear Schrodinger equation in Jacobi coordinates is solved by means of a coupled-channel expansion. Ligand deformation reduces the bending frequency by a few percent and increases the l-doubling constant q, while the stretching frequencies and rotational constants remain largely unchanged. For the first excited bending level, we predict ΔEJ=1 = 2q ≈ 24.9-26.4 MHz. These results establish LuOH+ as a viable platform for precision searches for C P -violating physics via the electron electric dipole moment and the nuclear magnetic quadrupole moment.