This paper reflects on the process of performing Thematic Analysis with Large Language Models (LLMs). Specifically, the paper deals with the problem of analytical saturation of initial codes, as produced by LLMs. Thematic Analysis is a well-established qualitative analysis method composed of interlinked phases. A key phase is the initial coding, where the analysts assign labels to discrete components of a dataset. Saturation is a way to measure the validity of a qualitative analysis and relates to the recurrence and repetition of initial codes. In the paper we reflect on how well LLMs achieve analytical saturation and propose also a novel technique to measure Inductive Thematic Saturation (ITS). This novel technique leverages a programming framework called DSPy. The proposed novel approach allows a precise measurement of ITS.