To understand this novel ground state of CeCuAl3, we have carried out low and high-energies inelastic neutron scattering (INS) measurements using the IRIS and HET spectrometers. Our studies revealed two well-resolved crystal field (CF) excitations at 1.25 meV (both on IRIS and HET) and 20.5 meV. We have also seen another INS peak ~ 9.8 meV in CeCuAl3, but this peak was not observed in LaCuAl3. As Ce ion in the tetragonal point symmetry can have a maximum of two CF excitations, the origin of 9.8 meV peak can only be understood by including coupling between the CF excitations and phonon. To confirm this conjuncture here we propose to carry out a detailed temperature dependence as well as wider Q-dependence (to study the form factor behaviour) study on CeCuAl3 using the HET spectrometer. We also propose to measure CeAuAl3 to check the possibility of spin-phonon coupling in this compound.