Grapheme-to-Phoneme (G2P) is an essential first step in any modern, high-quality Text-to-Speech (TTS) system. Most of the current G2P systems rely on carefully hand-crafted lexicons developed by experts. This poses a two-fold problem. Firstly, the lexicons are generated using a fixed phoneme set, usually, ARPABET or IPA, which might not be the most optimal way to represent phonemes for all languages. Secondly, the man-hours required to produce such an expert lexicon are very high. In this paper, we eliminate both of these issues by using recent advances in self-supervised learning to obtain data-driven phoneme representations instead of fixed representations. We compare our lexicon-free approach against strong baselines that utilize a well-crafted lexicon. Furthermore, we show that our data-driven lexicon-free method performs as good or even marginally better than the conventional rule-based or lexicon-based neural G2Ps in terms of Mean Opinion Score (MOS) while using no prior language lexicon or phoneme set, i.e. no linguistic expertise.