Most students I work with need 10-30 lessons. The amount is dependent on the musical background of the student and their ability to effectively study and practice on their own.
The AP Music Theory exam has several sections: multiple choice, sight singing, melodic and harmonic dictation, and three types of part writing. Students that have been successful at higher level musicianship and theory exams (for example Royal Conservatory or ABRSM), and are comfortable singing, will likely need fewer lessons. Students who have never taken a theory exam can still be successful, but they will likely need more lessons.