  We discuss junction conditions across null hypersurfaces in a class of
scalar-tensor gravity theories with i) second order dynamics, ii) obeying the
recent constraints imposed by gravitational wave propagation, and iii) allowing
for a cosmologically viable evolution. These requirements select kinetic
gravity braiding models with linear kinetic term dependence and scalar
field-dependent coupling to curvature. We explore a pseudo-orthonormal tetrad
and its allowed gauge fixing, with one null vector standing as the normal, the
other being transversal to the hypersurface. We derive a generalization of the
Lanczos equation in a 2+1 decomposed form, relating the energy density, current
and isotropic pressure of a distributional source to the jumps in the
transverse curvature and transverse derivative of the scalar. Additionally we
discuss a scalar junction condition and its implications for the distributional
source.
