Yes. Lying requires being able to discern truth from falsity. But LLMs don't know what's true even when they say true things. That's why "hallucinate" is a better word ... better but not perfect because for an LLM it's all hallucinations all the time. Some of those hallucinations (most of them) happen to turn out to be true.
(Note: I'm taking Google Alerts & Ego Salve as an ironic agent of Ted Nelson's concept of intertwingularity.)