  We study minimizers of the Lawrence--Doniach energy, which describes
equilibrium states of superconductors with layered structure, assuming
Floquet-periodic boundary conditions. Specifically, we consider the effect of a
constant magnetic field applied obliquely to the superconducting planes in the
limit as both the layer spacing $s\to 0$ and the Ginzburg--Landau parameter
$\kappa=\eps^{-1}\to\infty$, under the hypotheses that $s=\eps^\alpha$ with
$0<\alpha<1$. By deriving sharp matching upper and lower bounds on the energy
of minimizers, we determine the lower critical field and the orientation of the
flux lattice, to leading order in the parameter $\eps$. To leading order, the
induced field is characterized by a convex minimization problem in $\RR^3$. We
observe a ``flux lock-in transition'', in which flux lines are pinned to the
horizontal direction for applied fields of small inclination, and which is not
present in minimizers of the anisotropic Ginzburg--Landau model. The energy
profile we obtain suggests the presence of ``staircase vortices'', which have
been described qualitatively in the physics literature.
