Lamberth trial is not about nws, it's about fees beginning 2016. This case has already gone to scotus and sent back to district court. No more returns to scotus.
Lamberth's case is only about money damages at this point. He can't unwind the NWS because the only claim that survived doesn't ask him to.
Whoever loses at trial will (100% in my opinion) appeal the verdict to the Federal Circuit. Then whoever loses there will (100% in my opinion) appeal to the Supreme Court.
The Federal Circuit would probably take around a year to rule after briefing and oral arguments, perhaps longer if an en banc panel is requested following their ruling. Then a petition to the Supreme Court would be ruled on in maybe 6 months. If the Supreme Court denies cert, we could have a final ruling some time in mid to late 2024. If they grant it, add another 6 months to a year.
I'll defer to familymang's timeline here, he keeps track of this far better than I do.