  We study the \L ojasiewicz exponent and the log canonical threshold of ideals
of $\mathcal O_n$ when restricted to generic subspaces of $\mathbb C^n$ of
different dimensions. We obtain effective formulas of the resulting numbers for
ideals with monomial integral closure. An inequality relating these numbers is
also proven. We also introduce the notion of bi-Lipschitz equivalence of ideals
and we prove the bi-Lipschitz invariance of \L ojasiewicz exponents and log
canonical thresholds of ideals.
