Resonance energies Eλ, neutron widths Γn,λ, and radiation widths Γγ,λ for the compound system $^{175}$Lu+n were determined up to 1 keV from time-of-flight data reported in literature and recently measured at the GELINA facility of JRC-Geel (Belgium). The statistical analysis of the obtained resonance parameters provides an s-wave neutron strength function [S0=1.96(8)], mean level spacing [D0=3.24(9)eV], and average radiation width (〈Γγ0〉=61.3(59)meV) which are substantially different from those compiled in libraries dedicated to statistical calculations. The largest difference lies on the average radiation width, for which a value of 77(5) meV is recommended. $^{175}$Lu neutron cross sections were calculated with the talys code by using our s-wave average parameters as constraints. At kT=30keV, we obtain a total neutron capture cross section equal to 1125(62) mbarns, confirming the lower values reported in the 1990s.