  We present the first supertagging-based parser for LCFRS. It utilizes neural
classifiers and tremendously outperforms previous LCFRS-based parsers in both
accuracy and parsing speed. Moreover, our results keep up with the best
(general) discontinuous parsers, particularly the scores for discontinuous
constitutents are excellent. The heart of our approach is an efficient
lexicalization procedure which induces a lexical LCFRS from any discontinuous
treebank. It is an adaptation of previous work by M\"orbitz and Ruprecht
(2020). We also describe a modification to usual chart-based LCFRS parsing that
accounts for supertagging and introduce a procedure for the transformation of
lexical LCFRS derivations into equivalent parse trees of the original treebank.
Our approach is implemented and evaluated on the English Discontinuous Penn
Treebank and the German corpora NeGra and Tiger.
