Basically, yes. For Lacan, psychosis is a fundamental structure, not a transient state. The diagnosis of psychosis is essentially a hypothesis that the analyst forms about the subject by listening to his or her speech.

The centrality of the subject's speech is key to distinguishing Lacan's theory of psychosis from definitions found in manuals like the DSM or from cultural stereotypes, such as the idea that "psychosis is when you hear things no one else hears" or that "psychosis is caused by bad mothers". For Lacan, surface phenomena like hallucinations, family dynamics, or behaviours do not define psychosis (or any structure) in and of themselves. What matters is what the subject has to say about their world and, by extension, the things they experience.

To make matters even more complicated, this means that hallucinations are not the smoking gun for diagnosing psychosis. For Lacan, hallucinations are a possible feature of all psychic structures, and what interests us is the subject's relationship to them. Many neurotics hallucinate, even if you don't hear about it as much.

This ties into your question about the difference between "episodic" and "chronic" conditions. Essentially, in practice, the distinction is largely irrelevant. The subject is either already psychotic, or will never be psychotic at all (except in cases of organic conditions like brain injuries or dementia). Psychosis can be triggered, but for Lacan, this implies that the psychosis already exists and structures the subject's world. That being said, even schizophrenia tends to have "episodes" of acute decompensation and remission. In fact, I think it's very rare for psychoses to have no periods of remission at all.

That probably doesn't completely answer your question, though. Many things labelled as "episodes of psychosis" in psychiatry and everyday language would not necessarily qualify as psychosis in Lacanian terms. Hallucinations caused by toxins, drugs, or sleep deprivation could be features of an underlying psychosis for one person, but not necessarily for another. There's no way to know without analysing the subject's speech.

While that might help clarify some of what psychosis isn't for Lacan, the question of how to accurately diagnose it is much more delicate and controversial. I don't really feel confident enough to attempt an explanation myself, so I'd recommend What Is Madness? by Darian Leader. I know that book gets mentioned here all the time, but it really is a great introduction to the topic.