Large language models (LLMs) are increasingly adopted in educational contexts to provide personalized support to students and teachers. The unprecedented capacity of LLM-based applications to understand and generate natural language can potentially improve instructional effectiveness and learning outcomes, but the integration of LLMs in education technology has renewed concerns over algorithmic bias, which may exacerbate educational inequalities. Building on prior work that mapped the traditional machine learning life cycle, we provide a framework of the LLM life cycle from the initial development of LLMs to customizing pre-trained models for various applications in educational settings. We explain each step in the LLM life cycle and identify potential sources of bias that may arise in the context of education. We discuss why current measures of bias from traditional machine learning fail to transfer to LLM-generated text (e.g., tutoring conversations) because text encodings are high-dimensional, there can be multiple correct responses, and tailoring responses may be pedagogically desirable rather than unfair. The proposed framework clarifies the complex nature of bias in LLM applications and provides practical guidance for their evaluation to promote educational equity.