Rank 1 deformations of non-cocompact hyperbolic lattices

Let $X$ be a negatively curved symmetric space and $\mathrm{\Gamma }$ a non-cocompact lattice in $\mathrm{I}\mathrm{s}\mathrm{o}\mathrm{m}(X)$. We show that small, parabolic-preserving deformations of $\mathrm{\Gamma }$ into the isometry group of any negatively curved symmetric space containing $X$ remain discrete and faithful (the cocompact case is due to Guichard). This applies in particular to a version of Johnson-Millson bending deformations, providing for all $n$ infnitely many non-cocompact lattices in $\mathrm{S}\mathrm{O}(n,1)$ which admit discrete and faithful deformations into $\mathrm{S}\mathrm{U}(n,1)$. We also produce deformations of the figure-8 knot group into $\mathrm{S}\mathrm{U}(3,1)$, not of bending type, to which the result applies.