  The identification of strong gravitational lenses in large surveys has
historically been a rather time consuming exercise. Early data from the
Herschel Astrophysical Terahertz Large Area Survey (Herschel-ATLAS) demonstrate
that lenses can be identified efficiently at submillimetre wavelengths using a
simple flux criteria. Motivated by that development, this work considers the
statistical properties of strong gravitational lens systems which have been,
and will be, found by the Herschel-ATLAS. Analytical models of lens statistics
are tested with the current best estimates for the various model ingredients.
These include the cosmological parameters, the mass function and the lens
density profile, for which we consider the singular isothermal sphere (SIS) and
the Navarro, Frenk & White (NFW) approximations. The five lenses identified in
the Herschel-ATLAS Science Demonstration Phase suggest a SIS density profile is
preferred, but cannot yet constrain \Omega_\Lambda to an accuracy comparable
with other methods. The complete Herschel-ATLAS data set should be sufficient
to yield competitive constraints on \Omega_\Lambda. Whilst this huge number of
lenses has great potential for constraining cosmological parameters, they will
be most powerful in constraining uncertainty in astrophysical processes.
Further investigation is needed to fully exploit this unprecedented data set.
