  J/psi-pair production at the LHC is currently one of the few tools available
to probe gluon transverse momentum distributions (TMDs). In this context, data
from LHCb in the collider mode have the potential to probe the evolution of the
unpolarised-gluon TMDs and to measure the distribution of the
linearly-polarised gluon in unpolarised protons for the first time. In this
proceedings contribution, improved predictions obtained for the LHC (at sqrt(s)
= 13 TeV) up to next-to-leading logarithm (NLL) in TMD factorisation are
presented. We show the obtained predictions of transverse-momentum
distributions at different invariant masses and rapidities computed in the LHCb
acceptance along with PDF uncertainty. We predict the azimuthal modulations of
the cross section that arise from linearly-polarised gluons.
