A behavior of the measurement error of the average Doppler frequency as a function of parameters of the turbulent atmosphere and technical parameters of the Doppler lidar is considered based on the maximum likelihood method and statistical theory for estimating the random process parameters. It is shown that the measurement error of the average Doppler frequency first decreases and reaches the minimum point, then it increases with an increase of the scattering volume length for a locally-isotropic model of the turbulence corresponding to the `2/3 law'. The value of the scattering volume length which corresponds to the minimum measurement error depends on the energy dissipation rate and technical parameters of the Doppler lidar: the signal-to-noise ratio, time of sample, and number of samples. The results of this paper are in agreement with the results published in Ref. 1 - 7 in limiting cases.