  We investigate a recently proposed UV-complete composite Higgs scenario in
the light of the first LHC runs. The model is based on a $SU(4)$ gauge group
with global flavour symmetry breaking $SU(5) \to SO(5)$, giving rise to pseudo
Nambu-Goldstone bosons in addition to the Higgs doublet. This includes a real
and a complex electroweak triplet with exotic electric charges. Including
these, as well as constraints on other exotic states, we show that LHC
measurements are not yet sensitive enough to significantly constrain the
model's low energy constants. The Higgs potential is described by two
parameters which are on the one hand constrained by the LHC measurement of the
Higgs mass and Higgs decay channels and on the other hand can be computed from
correlation functions in the UV-complete theory. Hence to exclude the model at
least one constant needs to be determined and to validate the Higgs potential
both constants need to be reproduced by the UV-theory. Due to its
UV-formulation, a certain number of low energy constants can be computed from
first principle numerical simulations of the theory formulated on a lattice,
which can help in establishing the validity of this model. We assess the
potential impact of lattice calculations for phenomenological studies, as a
preliminary step towards Monte Carlo simulations.
