Data-driven grammar induction aims at producing wide-coverage grammars of human languages. Initial efforts in this field produced relatively shallow linguistic representations such as phrase-structure trees, which only encode constituent structure. Recent work on inducing deep grammars from treebanks addresses this shortcoming by also recovering non-local dependencies and grammatical relations. My aim is to investigate the issues arising when adapting an existing Lexical Functional Grammar (LFG) induction method to a new language and treebank, and find solutions which will generalize robustly across multiple languages. The research hypothesis is that by exploiting machine-learning algorithms to learn morphological features, lemmatization classes and grammatical functions from treebanks we can reduce the amount of manual specification and improve robustness, accuracy and domain- and language -independence for LFG parsing systems. Function labels can often be relatively straightforwardly mapped to LFG grammatical functions. Learning them reliably permits grammar induction to depend less on language-specific LFG annotation rules. I therefore propose ways to improve acquisition of function labels from treebanks and translate those improvements into better-quality f-structure parsing. In a lexicalized grammatical formalism such as LFG a large amount of syntactically relevant information comes from lexical entries. It is, therefore, important to be able to perform morphological analysis in an accurate and robust way for morphologically rich languages. I propose a fully data-driven supervised method to simultaneously lemmatize and morphologically analyze text and obtain competitive or improved results on a range of typologically diverse languages.