  In this paper we introduce the SEAGLE (i.e. Simulating EAGLE LEnses) program,
that approaches the study of galaxy formation through strong gravitational
lensing, using a suite of high-resolution hydrodynamic simulations, Evolution
and Assembly of GaLaxies and their Environments (EAGLE) project. We introduce
the simulation and analysis pipeline and present the first set of results from
our analysis of early-type galaxies. We identify and extract an ensemble of
simulated lens galaxies and use the GLAMER ray-tracing lensing code to create
mock lenses similar to those observed in the SLACS and SL2S surveys, using a
range of source parameters and galaxy orientations, including observational
effects such as the Point-Spread-Function (PSF), pixelization and noise levels,
representative of single-orbit observations with the Hubble Space Telescope
(HST) using the ACS-F814W filter. We subsequently model these mock lenses using
the code LENSED, treating them in the same way as observed lenses. We also
estimate the mass model parameters directly from the projected surface mass
density of the simulated galaxy, using an identical mass model family. We
perform a three-way comparison of all the measured quantities with real lenses.
We find the average total density slope of EAGLE lenses, $t=2.26\; (0.25\;
\rm{rms})$ to be higher than SL2S, $t=2.16$ or SLACS, $t=2.08$. We find a very
strong correlation between the external shear ($\gamma$) and the complex
ellipticity ($\epsilon$), with $\gamma \sim \epsilon/4$. This correlation
indicates a degeneracy in the lens mass modeling. We also see a dispersion
between lens modeling and direct fitting results, indicating systematical
biases.
