  An angular analysis of Lambda_b0 -> J/psi Lambda decays is performed using a
data sample corresponding to 1.0 fb^{-1} collected in pp collisions at sqrt(s)
= 7 TeV with the LHCb detector at the LHC. A parity violating asymmetry
parameter characterising the Lambda_b0 -> J/psi Lambda decay of 0.05 +/- 0.17
+/- 0.07 and a Lambda_b0 transverse production polarisation of 0.06 +/- 0.07
+/- 0.02 are measured, where the first uncertainty is statistical and the
second systematic.
