  Rare $b \to s\ell^+\ell^-$ flavour-changing-neutral-current processes provide
important tests of the Standard Model of particle physics. Angular observables
in exclusive $b \to s\ell^+\ell^-$ processes can be particularly powerful as
they allow hadronic uncertainties to be controlled. Amongst the exclusive
processes that have been studied by experiments, the decay $\Lambda_b\to
\Lambda\ell^+\ell^-$ is unique in that the $\Lambda_b$ baryon can be produced
polarised. In this paper, we derive an expression for the angular distribution
of the $\Lambda_b\to \Lambda\ell^+\ell^-$ decay for the case where the
$\Lambda_b$ baryon is produced polarised. This extends the number of angular
observables in this decay from 10 to 34. Standard Model expectations for the
new observables are provided and the sensitivity of the observables is explored
under a variety of new physics models. At low-hadronic recoil, four of the new
observables have a new short distance dependence that is absent in the
unpolarised case. The remaining observables depend on the same short distance
contributions as the unpolarised observables, but with different dependence on
hadronic form-factors. These relations provide possibilities for novel tests of
the SM that could be carried out with the data that will become available at
the LHC or a future $e^+e^-$ collider.
