While applications of live programming are expanding to more practical and professional domains, most live programming environments (LPEs) are still developed for a single target language with an original code editor. We propose an implementation framework for developing LPEs so that we can minimize efforts on implementing an LPE for a different target language and for an existing code editor/IDE. Our idea is to use a meta-JIT language implementation framework (e.g., Graal/Truffle and RPython) and the Language Server Protocol (LSP) to separate core live programming implementations from language specific and editor/IDE specific implementations. This paper takes the Kanon live programming environment as a concrete example, and discusses how we can design the framework to accommodate the features of Kanon. Although the framework design is still underway, the paper presents a sketch of the framework APIs for separating language specific functions, and clarifies the requirements to LSP.