We study the electronic and phononic excitations of heavy-fermion metal CeCoIn5 by polarization- resolved Raman spectroscopy to explore the Kondo-lattice coherence. Below the coherence tempera- ture T* = 45 K, the continuum of electronic excitations in the XY scattering geometry is suppressed at frequencies below 50cm-1, whereas the low-frequency continuum in the X’Y’ geometry exhibits no change across T*. We relate the suppression to the reduced electron-electron scattering rate resulting from the coherence effect. The presence of suppression in the XY geometry and absence of it in the X’Y’ geometry implies that the α and β bands become coherent below T*, whereas the γ band remains largely incoherent down to 10 K. Moreover, two optical phonon modes exhibit anomalies in their temperature dependence of the frequency and linewidth below T*, which results from developing coherent spectral weight near the Fermi level and reduced electron-phonon scattering rate. Our results further support the key role of anisotropic hybridization in CeCoIn5.