There is only one file type that uses the .LEX extension:
Adobe Linguistic Library Data File
A LEX file is a lexicon data file created by Linguistic Library, an Adobe development kit used to add linguistic services, such as spelling and grammar checkers, to Adobe products. It contains the shared lexicons, or words and their syntax, for a language. LEX files are used to store language-specific data for document validation in Adobe products.
LEX files can be used across multiple Adobe products, including Acrobat, Photoshop, InDesign, and Illustrator.
Updated: July 19, 2018