Large Language Models (LLMs) have taken the field of AI by storm, but their adoption in the field of Artificial Life (ALife) has been, so far, relatively reserved. In this work we investigate the potential synergies betweens LLMs and ALife, drawing on a large body of research in the two fields. We explore the potential of LLMs as tools for ALife research, for example, as operators for evolutionary computation or the generation of open-ended environments. Reciprocally, principles of ALife, such as self-organization, collective intelligence and evolvability can provide an opportunity for shaping the development and functionalities of LLMs, leading to more adaptive and responsive models. By investigating this dynamic interplay, the paper aims to inspire innovative crossover approaches for both ALife and LLM research. Along the way, we examine the extent to which LLMs appear to increasingly exhibit properties such as emergence or collective intelligence, expanding beyond their original goal of generating text, and potentially redefining our perception of lifelike intelligence in artificial systems.