The tests change from year to year, but I would say there are probably 2-3 questions that might directly ask about the Lagrangian formalism of classical mechanics. https://www.ets.org/gre/subject/about/content/physics
says that classical mechanics is 20% of the exam (i.e. ~20 questions) but this is a giant topic in which Lagrangian mechanics is just a small part. My advice is that it would be useful to know the following:
1. How to write the Lagrangian (practice on a few basic systems like a pendulum)
2. How to derive the equations of motions from the Lagrangian
3. What "action" means
4. Noether's theorem (i.e. symmetries in a system leads to conserved quantities)
I think just these basic things that you might have already covered is about the depth you'd need for most Lagrangian questions. Sure, there may be an occasional advanced question in some tests, but it's generally not worth it, in my opinion, to prepare for every advanced question possible. I would spend the additional hours making sure the other 90% of the test is well known and take the gamble that the 10% "advanced questions" would be in things I have more experience in. But that's just me.