Lexicalized parsing aims at building a tree structure from a set of tokens. So a correctly parsed sentence could for example return two sub phrases, so the syntactical structure of the sentence is identified.
Dependency parsing however, aims at finding relations between the words. For example, consider the sentence "I have never ever seen this before". A dependency parser could find a (directed) auxiliary relation from "have" to "seen". So a dependency parsing indicates the (grammatical) relations between
This is a rather informal explanation but maybe you can make some use of it.