This paper presents a first efficient implementation of a weighted deductive CYK parser for Probabilistic Linear ContextFree Rewriting Systems (PLCFRS), together with context-summary estimates for parse items used to speed up parsing. LCFRS, an extension of CFG, can describe discontinuities both in constituency and dependency structures in a straightforward way and is therefore a natural candidate to be used for data-driven parsing. We evaluate our parser with a grammar extracted from the German NeGra treebank. Our experiments show that datadriven LCFRS parsing is feasible with a reasonable speed and yields output of competitive quality.