The mixed spin chain compound, LiCuFe2(VO4)(3), reaches a magnetically ordered state in two steps at T-N2 = 9.8 K and T-N1 = 8.2 K detected in magnetic-susceptibility chi and specific-heat C-p measurements. Dielectric permittivity epsilon evidences these transitions by a sharp peak at T-N2 and a steplike anomaly at T-N1, both easily suppressed by an external magnetic field. These features in permittivity are preceded by a frequency-dependent relaxation-type anomaly at T* insensitive to the magnetic field. Mossbauer spectroscopy reveals a wide distribution of a hyperfine field between T-N2 and T-N1 while the first-principles calculations provide values of magnetic-exchange-interaction parameters. For Cu, the orbital moment aligned in the same direction as the spin moment is substantial. This large orbital moment is important in driving the polarization through an inverse Dzyaloshinksii-Moriya interaction in a situation where the spatial symmetry gets broken in the magnetic structure. The data obtained suggest the spin-order-induced ferroelectricity is inherent for improper multiferroics.