  In the context of the currently ongoing efforts to improve the accuracy and
reliability of the measurement of the Lense-Thirring effect in the
gravitational field of the Earth it has recently been proposed to use the data
from the existing spacecraft endowed with some active mechanisms of
compensation of the non-gravitational accelerations like GRACE. In this paper
we critically discuss this interesting possibility. Unfortunately, it turns out
to be unpracticable because of the impact of the uncancelled even zonal
harmonic coefficients of the multipolar expansion of the terrestrial
gravitational potential and of some time-dependent tidal perturbations which
would resemble as superimposed linear trends over the necessarily limited
observational time span of the analysis.
