lambda-(BETS)2GaCl4 is a non-magnetic anion-based organic superconductor SC attracting interest since its Fe analog becomes SC by applying 33 T. Both SCs have similar Tc ~5 K. We measured TF=30&60 G and ZF-μSR down to 0.3K on powder sample. In order to achieve more information about superconducting pairing symmetry from different angles, we measured TF dependence of the damping rate of the muon spin precession s(B), up to 70 G. This measurement is important to investigate the field dependence of the penetration depth, to discuss the Cooper pairing symmetry and to search nonlocal effects. Such kind of measurement has never been done in the past. Due to the narrower TF region and large error bars, the s(B) is still unsure. Accordingly, we have got a strong requirement to carry out the same experiments in the higher TF down to mK range in order to satisfy our questions on this SC.