This is interesting, and I like the systematic approach taken! (I currently haven't read very much, being still on the section for verbs, and I am just writing some first impressions here given what I know.) I will definitely remember, for example, the distinctions between static and dynamic verbs and between patient-oriented and agent-oriented verbs. The promises of being able to use this system to derive many words from a small number of roots is appealing to me—I like languages that minimize the amount of information that needs to be memorized.
I still feel like I don't completely understand the distinction between patient in focus. To me, all participants in a verb can be said to be in a state or state change, namely the state of being a participant in the verb.
For example, "John looked at the mouse" is said to be AP/F-s, with John being the agent and patient while the mouse is the focus. But you can also say that the mouse is in the state of "being looked at", so why shouldn't the mouse be the patient? It seems to me that an explanation for John being the patient might be that his state of looking at something is more natural and less contrived to think about than the mouse's state of being looked at. But if I were to make these judgements about contrivedness, I don't think I could consistently tell the difference between a concept seeming contrived just because it happens to be complicated to express in English (and other languages I know), versus the concept genuinely being contrived in most people's minds regardless of language.
A similar example: is "The rabbit eats the carrot" AP/F or A/P? Certainly the carrot's state is being affected by this action. You can say that the rabbit is the patient because it is in the state of eating, or the carrot is the patient because it is in the state of being eaten.
There are also some predicates that are symmetric in their arguments, which seem to naturally have two patients. For example, with "is a parent of" and "is a child of"—an instance of X being a parent of Y is the same thing as an instance of Y being a child of X. Similarly, "above" and "below" are related in this way. To me it seems kind of arbitrary to choose one of the arguments as the patient and the other as the focus, since semantically they play the same kind of role. The predicate "is a sibling of" furthermore has both arguments playing the exact same role and being swappable with each other. I do like Latejami for giving semantic criteria to help you determine which role an argument plays in a predicate rather than just arbitrarily assigning roles like "the first argument", "the second argument", etc., but it feels like such semantic criteria break down here.
I also wonder how Latejami deals with verbs like "bet" that seem to want to take two focuses. In "I bet you thirty dollars that they'll win", "thirty dollars" and "that they'll win" seem to both want to be focuses. (See also: the discussion on quaternary predicates in this forum.) I have read that Latejami breaks down certain ditransitive verbs like "exchange" into two transitive verbs describing each side of the exchange, but I don't yet know exactly how this is done, and whether it's done to "bet" as well. In my mind, I like "exchange" and "bet" having four arguments, and it seems arbitrary to me to restrict verbs to not be able to have multiple focuses (or multiple patients). However, the restriction of verbs to have a single focus does seem to be useful in the vast majority of cases—I remember it being written that the focus actually plays many distinct roles in different predicates, but it's okay to merge them together because it's very rare that more than one of these roles shows up in a single predicate.
Overall, though: I find this language very valuable. Rick Morneau's list of essays on language design calls Latejami's reference manual "a complete monograph on the topic of word design", and I think this description shows Latejami's usefulness. The reference manual is not only a document about the language itself, but is also a great resource for anyone trying to make a language with similar goals as Latejami. Some of the concerns I raised above are just things I don't yet understand, and might be resolved simply by me reading more; other concerns I have may be things I would try to do differently if I were designing a language with the goals of Latejami. But ultimately, the reference manual has provided me a lot of clarity about how lexicons may be structured in a systematic and regular way.