There's 1 seat LHR-TYO tomorrow in F, otherwise nothing for months, although stuff should continually open up - with absolutely no guarantee - as JAL tend to release unsold revenue F seats to partner award availability a few days in advance of travel. It is impossible to depend on this though, especially for more than 1 seat, and it has varied greatly in the past month.

As I say, I haven't seen more than 1 seat in F on JAL per flight, even close to the time, for a while and there may be an internal policy against higher numbers due to recent events. Happy to be corrected on this, it may be the tools I'm using. [Edit: JAL seem to be back to releasing more than 1 F seat, at least near to flight dates.]

Lots more business class availability direct.

Final point: one needs to search direct flights only, because the AA award engine hallucinates JAL availability when connections are involved. For example, for LHR-TYO with connections allowed, it will propose a connection to Paris and then imagine a JAL F segment from Paris which doesn't exist etc, or vice-versa CDG-TYO via LHR. This is reflected in every external tool that uses American's API.