  We attempt to explain recent anomalies in semileptonic $B$ decays at LHCb via
a composite Higgs model, in which both the Higgs and an $SU(2)_L$-triplet
leptoquark arise as pseudo-Goldstone bosons of the strong dynamics. Fermion
masses are assumed to be generated via the mechanism of partial compositeness,
which largely determines the leptoquark couplings and implies non-universal
lepton interactions. The latter are needed to accommodate tensions in the $b
\to s \mu \mu$ dataset and to be consistent with a discrepancy measured at LHCb
in the ratio of $B^+ \to K^+ \mu^+ \mu^-$ to $B^+ \to K^+ e^+ e^-$ branching
ratios. The data imply that the leptoquark should have a mass of around a TeV.
We find that the model is not in conflict with current flavour or direct
production bounds, but we identify a few observables for which the new physics
contributions are close to current limits and where the leptoquark is likely to
show up in future measurements. The leptoquark will be pair-produced at the LHC
and decay predominantly to third-generation quarks and leptons, and LHC13
searches will provide further strong bounds.
