  The cancelation of the first even zonal harmonic coefficient J2 of the
multipolar expansion of the Newtonian part of the Earth's gravitational
potential from the linear combination f(2L) of the nodes of LAGEOS and LAGEOS
II used in the latest tests of the general relativistic Lense-Thirring effect
cannot be perfect, as assumed so far. It is so, among other things, because of
the uncertainties in the spatial orientation of the terrestrial spin axis as
well. As a consequence, the coefficient c1 entering f(2L), which is not a
solve-for parameter being theoretically computed from the analytical
expressions of the classical node precessions due to J2, is, on average,
uncertain at a 10-8 level over multi-decadal time spans DT comparable to those
used in the data analyses performed so far. A further \simeq 20% systematic
uncertainty in the theoretically predicted gravitomagnetic signal, thus,
occurs. The shift due to the gravitomagnetic frame-dragging on the
station-spacecraft range is numerically computed over DT = 15 d and DT = 1 yr.
The need of looking at such a directly observable quantity is pointed out,
along with some critical remarks concerning the methodology used so far to
measure the Lense-Thirring effect with the LAGEOS satellites. Suggestions for a
different, more trustable and reliable approach are offered.

General Relativity and Quantum Cosmology;Earth and Planetary Astrophysics;Space Physics