It is said lexical stress is word stress, but I don't understand why they named it differently.
Metrical stress refers to a specific family of generative theories of stress, originating from a proposal by Liberman and Prince 1977. It has various technical characteristics as to what it claims "stress" is. Lexical stress or word stress refers to the language fact, not the theoretical analysis, and specifically refers to the fact about single words as opposed to stress at the level of the sentence (where you have to deal with chances in stress level as a function of the phrasal construction – eg. light (housekeeper) versus (lighthouse) keeper). Word stress is simply the stress of a word, regardless of the rule or lack of rule. Lexical stress refers to the fact that in some languages (English, Russian) you have to memorize where the stress is, as determined by what lexical item you are talking about (permít, pérmit). In many other languages (Arabic, Finnish, Czech) the position of stress in the word is entirely predictable, and need not be entered in the lexicon. However, especially owing to the theory of Lexical Phonology, such stress systems could be called "lexical stress" because at the end of the lexical phonology, a predictable stress is added to the entire word (but not including any influence of other words).