This study provides a comprehensive insight into the effects of controlled off-stoichiometry on the structural and multiferroic properties of the hexagonal manganite LuMn_1−xO_3+δ (x = 0.02; δ ∼ 0), supported by neutron powder diffraction measurements confirming single phase P6₃cm symmetry and evidencing a relevant ferromagnetic component, below T_N ∼ 90 K, which breaks the archetypal geometrically frustrated antiferromagnetic state typically ascribed to LuMnO₃. The perturbations in the triangular disposition of spins prompt an additional electric polarization contribution and a clear enhancement of the magnetoelectric coupling which are in good agreement with the results of first principles calculations. In addition, Raman spectroscopy, dielectric permittivity, pyroelectric current and magnetic measurements as a function of temperature point out the precursor effects of the magnetic phase transitions involving a strong coupling between spins, lattice and electric order, even above the Néel temperature.