  The laser-tracked geodetic satellites LAGEOS, LAGEOS II and LARES are
currently employed, among other things, to measure the general relativistic
Lense-Thirring effect in the gravitomagnetic field of the spinning Earth with
the hope of providing a more accurate test of such a prediction of the
Einstein's theory of gravitation than the existing ones. The secular decay
$\dot a$ of the semimajor axes $a$ of such spacecrafts, recently measured in an
independent way to a $\sigma_{\dot a}\approx 0.1-0.01$ m yr$^{-1}$ accuracy
level, may indirectly impact the proposed relativistic experiment through its
connection with the classical orbital precessions induced by the Earth's
oblateness $J_2$. \textcolor{black}{Indeed,} the systematic bias due to the
current measurement errors $\sigma_{\dot a}$ is of the same order of magnitude
of, or even larger than, the expected relativistic signal itself; moreover, it
grows linearly with the time span $T$ of the analysis.
\textcolor{black}{Therefore, the parameter-fitting algorithms must be properly
updated in order to suitably cope with such a new source of systematic
uncertainty. Otherwise,} an improvement of one-two orders of magnitude in
measuring the orbital decay of the satellites of the LAGEOS family would be
required to reduce this source of systematic uncertainty to a percent fraction
of the Lense-Thirring signature.
