  We consider Lipschitz percolation in $d+1$ dimensions above planes tilted by
an angle $\gamma$ along one or several coordinate axes. In particular, we are
interested in the asymptotics of the critical probability as $d \to \infty$ as
well as $\gamma \to \pi/4.$ Our principal results show that the convergence of
the critical probability to 1 is polynomial as $d\to \infty$ and $\gamma \to
\pi/4.$ In addition, we identify the correct order of this polynomial
convergence and in $d=1$ we also obtain the correct prefactor.
