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This paper shows that training a lexicalized parser on a lemmatized morphologically-rich treebank such as the French Treebank slightly improves parsing results. We also show that lemmatizing a similar in size subset of the English Penn Treebank has almost no effect on parsing performance with gold lemmas and leads to a small drop of performance when automatically assigned lemmas and POS tags are used. This highlights two facts: (i) lemmatization helps to reduce lexicon data-sparseness issues for French, (ii) it also makes the parsing process sensitive to correct assignment of POS tags to unknown words.