  Line intensity mapping offers a new avenue for constraining cosmological
parameters in the high redshift Universe. However measurements of the growth of
structure, a sensitive probe of gravity, are affected by a well known
degeneracy with astrophysical parameters, encoded in the mean brightness
temperature of the specific line. In this work we show how to break this
degeneracy, to a level that could allow constraints of the amplitude of
cosmological fluctuations at the percent level, using information in the mildly
non-linear regime of structure formation as described by Lagrangian
Perturbation Theory. We focus on the 21-cm line with forecasts for HIRAX and
the proposed Stage II experiment as illustrations.
