The analytic expression of gain for both frequencies in non-steady state waveguidefree electron lasers is derived by taking into account axial energy spread of electron beams. The approximate explicit expression is also given. They agree well with numericalsimulations. Based on the non-steady state gain, the necessary detuning of cavity length tocounteract the effect of lethargy is estimated, and the mechanism of self mode--locking isexplained clearly in time domain.