We present the ground and excited state spectra of Omega(0)(c) baryons with spin up to 7/2 from lattice quantum chromodynamics with dynamical quark fields. Based on our lattice results, we predict the quantum numbers of five Omega(0)(c) baryons, which have recently been observed by the LHCb Collaboration. Our results strongly indicate that the observed states Omega(c)(3000)(0) and Omega(c)(3050)(0) have spin-parity J(P) = 1/2(-), the states Omega(c)(3066)(0) and Omega(c)(3090)(0) have J(P) = 3/2(-), whereas Omega(c)(3119)(0) is possibly a 5/2(-) state.