FRA T2 departures are split into 2 levels, the lower level is schengen and the upper level is non-schengen. The latter has better facillities.
I have never changed only in T2 in Frankfurt, so I don't know what the route is, and you don't mention where you come from. But even if you go out of departures fully and back in again it won't take long as its a small terminal with short-ish walking distances.
FRA T2 lounges are pre-security (for non-schengen at least) but post passport check.
But the security is done by a block of gates, so tends to be quick as often there is just 1 or 2 flights scheduled from those gates at a time. And I think (but you need to check) that they call the flights from the lounge.
BA use the JAL lounge, I don't know if you can get in the cathay lounge or not, but that is on the other side of T2. The JAL lounge is opposite the gates where the BA flights depart from.
Whenever I have taken the flight then it was always a SH 767, but I haven't done this flight often (I am actually booked on it next week!). So I can't really offer an opinion on this.