Borocarbide superconductors, which are thought to be conventional BCS-type superconductors, are not so conventional in several electronic Raman properties. Anisotropic gap-like features and finite scattering strength below the gap were observed for the RNi2B2C (R = Lu, Y) systems in our previous study. The effects of Co-doping on the 2Δ gap-like features and the finite scattering strength below and above the gap are studied in R = Lu (B = B11) system. In superconducting states, Co-doping strongly suppresses the 2Δ peak in both B2g and B1g symmetries. Raman cross-section calculation which includes inelastic scattering shows a relatively good fit to the features above the 2Δ peak, while it does not fully account for the features below the peak.