The coherent emission of exciton polaritons was proposed as a means of lowering the lasing threshold because it does not require the dissociation of excitons to obtain an electron-hole plasma, as in a classical semiconductor laser based on population inversion. In this work we propose a method to prove clearly the polaritonic nature of lasing by combining experimental measurements with a model accounting for the permittivity change as a function of the carrier density. To do so we use angle resolved photoluminescence to observe the lasing at cryogenic temperature from a polariton mode in a zinc oxide waveguide structure, and to monitor the continuous shift of the polaritonic dispersion towards a photonic dispersion as the optical intensity of the pump is increased (up to 20 times the one at threshold). This shift is reproduced thanks to a model taking into account the reduction of the oscillator strength and the renormalization of the band gap due to the screening of the electrostatic interaction between electrons and holes. Furthermore, the measurement of the carrier lifetime at optical intensities in the order of those at which the polariton lasing occurs enables us to estimate the carrier density, confirming that it is lower than the corresponding Mott density for zinc oxide reported in the literature.