The word classis has, in classical Latin, a range of different definitions, namely (according to OLD):
1) a class of citizens on the basis of property.
2) a body of citizens summoned for military service
3) a naval force, a fleet
4) a class or grade, b) of pupils
5) a band, group, squad
The word is probably ultimately derived from the verb calo, 'summon', but a prominent semantic element of the word seems to be 'division', hence 1) and, what I'm interested in here, 4). Examples of 4b) are Quintilian 1.2.23 "cum pueros in classes distribuerant", i.e. the division of pupils based on their proficiency, and Quint. 10.5.21 "consuetuo classium certis diebus audiendarum", refering to such a division of the pupils, specifically to the group itself. This is, as far as I know, the only classical meaning of the word classis in connection with education.
In the modern languages, however, the cognates and borrowings of classis have very often taken on a further range of meanings. I have here looked at Italian (classe), Spanish (clase), French (classe) and English (class). In all these languages, the classical meaning is extant, namely
* a group of students that receive the same instructions.
The main other modern definitions, which exist in most, if not all, of these languages, but not in classical Latin, are
* the room where lessons are held, and, especially
* a lesson, such as the Spanish "una clase de historia".
I have now noticed how the word classis frequently is used for "lesson" in neo-Latin litterature: in Peter Needham's translations of Harry Potter and Traupman's Conversational Latin for Oral Proficiency, constructions such as "in classe alicuius magistri" (meaning "in or during the lesson(s) held by some teacher), "classem habere" (of pupils), and so on, are very common. But I wonder if this really is proper: in my ears they sound like anglicisms.
Well, what is proper? Now, I'm not necessarily advocating a strict Ciceronian Latin: I am not opposed to this usage in case it can be shown that it was used in medieval or later Latin, up to, say, the 18th century, and I would only be happy if someone can show that this is the case. But I fear -- I'm not sure -- that this usage is only a result of modern authors and translators, without a direct connection to a living Latin tradition, merely copying the modern idioms.
The purely classical term for "lesson" seems to be schola. But if this does not seem fitting for the lesson of the modern school-systems, there are many other words which could be used instead, such as (prae)lectio, recitatio, auditio or collegium. While not exactly having the meaning of "lesson" in classical Latin, any of these, in my opinion, would be better than classis.
But, as I said, I don't mind being proven wrong. What's the usual word for "lesson" in renaissance Latin, for example?