If things didn't look like they were progressing after the first season or even during the 2nd obviously the decision would have to be made.
The main problem in all of this is the owner and board affording managers the right time. We don't know what guarantees and assurances Lampard will be made. Me and most Chelsea fans would be happy to just see some of our youth players feature heavily but playing youth and winning trophies does not have to be exclusive from the other. Above all the main objective would just be to see the team progressing. Irrespective of Sarri's league finish and Europa League win, l thought we had made progress as a team, tactically, mentally and we were in a better shape compared to earlier in the season. If Sarri hadn't finished 3rd and/or didn't win that trophy, it's likely there would have been many calling for his head. I for one would have been happy to see Sarri continue even if say we finished 5th and didn't win the final because I saw some positive signs and potential in how we were progressing on the pitch.
On a personal level, I don't think we have many other options other than Lampard. Before considering Lampard, I would have had a punt on Erik Ten Hag if he could have been tempted. Allegri and Benitez would have been a step in the wrong direction, not to say they aren't decent managers.