1. You could remove "I used to" and keep "He always lies, so I don't believe him anymore." OR 2. I believe you meant "I am used to" (present simple + "used to" phrase) which means you are familiar with something. Change "he" to "him" pronoun and change "lies" to gerund "lying." (A gerund is a verb form that ends in -ing and functions as a noun in a sentence). "I used to" is best used when you are talking about something you did in the past but you don't do in the present. By using "I am used to him always lying," the subject is you and your experience and knowledge of his past and present actions of lying and because of that "I don't believe him anymore."