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Re:Amazon Lex – Conversational interfaces for your applications by nickmorri on Monday December 05, 2016 @05:33PM (#13110425)
I'm thinking it's a play on A(lex)a andlexical analysis[1]. That may be where Alexa got her name.

https://en.wikipedia.org/wiki/Lexical_analysis

Re:Amazon Lex – Conversational interfaces for your applications by OJFord on Monday December 05, 2016 @06:42PM (#13110953)
I assumed it was specifically from 'a lexer', an homonym.