  We consider transformations preserving a contracting foliation, such that the
associated quotient map satisfies a Lasota-Yorke inequality. We prove that the
associated transfer operator, acting on suitable normed spaces, has a spectral
gap (on which we have quantitative estimation). As an application we consider
Lorenz-like two dimensional maps (piecewise hyperbolic with unbounded
contraction and expansion rate): we prove that those systems have a spectral
gap and we show a quantitative estimate for their statistical stability. Under
deterministic perturbations of the system of size $\delta$, the physical
measure varies continuously, with a modulus of continuity $O(\delta \log \delta
)$, which is asymptotically optimal for this kind of piecewise smooth maps.
