  We comprehensively examine precision predictions for scalar leptoquark pair
production at the LHC. In particular, we investigate the impact of lepton
$t$-channel exchange diagrams that are potentially relevant in the context of
leptoquark scenarios providing an explanation for the flavour anomalies. We
also evaluate the corresponding total rates at the next-to-leading order in
QCD. Moreover, we complement this calculation with the resummation of
soft-gluon radiation at the next-to-next-to-leading logarithmic accuracy, hence
providing the most precise predictions for leptoquark pair production at the
LHC to date. Relying on a variety of benchmark scenarios favoured by the
anomalies, our results exhibit an interesting interplay between the $t$-channel
diagram contributions, the flavour texture satisfied by the leptoquark Yukawa
couplings, the leptoquark masses and their representations under the Standard
Model gauge group, as well as the chosen set of parton densities used for the
numerical evaluations. The net effect on a cross section turns out to be very
non-generic and ranges up to about 60% with respect to the usual
next-to-leading-order predictions in QCD (i.e. without any $t$-channel
contribution) for some scenarios considered. Dedicated calculations are thus
required for any individual leptoquark model that could be considered in a
collider analysis in order to assess the size of the studied corrections. In
order to facilitate such calculations we provide dedicated public numerical
packages.
