  Here we analyze in detail some aspects of the proposed use of Ajisai and
Jason-1, together with the LAGEOS satellites, to measure the general
relativistic Lense-Thirring effect in the gravitational field of the Earth. A
linear combination of the nodes of such satellites is the proposed observable.
The systematic error due to the mismodelling in the uncancelled even zonal
harmonics would be \sim 1% according to the latest present-day
CHAMP/GRACE-based Earth gravity models. In regard to the non-gravitational
perturbations especially affecting Jason-1, only relatively high-frequency
harmonic perturbations should occur: neither semisecular nor secular bias of
non-gravitational origin should affect the proposed combination: their maximum
impact is evaluated to \sim 4% over 2 years. Our estimation of the
root-sum-square total error is about 4-5% over at least 3 years of data
analysis required to average out the uncancelled tidal perturbations.
