Grammatical gender is the linguistic application of a male, female, or neuter categorization to nouns. This is a commonality in Romance languages such as Spanish and French. It is necessary that adjective that describe the nouns agree. Therefore the grammatical gender is applied to them as well.
For example: El gato negro (the male, black cat) vs. La gata negra (the female black cat)
As far as gender goes, it is the grammatical usage what transforms one word into another from neutral to masculine, or feminine. The lexical meaning of a word that has been transformed. Although there is no "lexical gender" per se, there is something called lexical density which often goes hand in hand with grammatical gender. Lexical density refers to the bulk of FUNCTIONAL words that are spoken during discourse, or in written language as opposed to auxiliary words. It is as if we sifted all the information that we process and filtered out only the words that imply meaning. If we apply this to grammatical gender, then it would entail that only functional words can be transformed into feminine or masculine.
Ex: El gato negro, the lexical density is in the words "gato" and "negro" because these are the words that actually provide you with information. This is what makes it be "lexical".