Agree that Lampard is safe, and that Pocchettino is unhappy (probably because - on the resources at his disposal, he has taken Spurs as far as they can ago; a place in the final of the CL last season strikes me as about as good as it is going to get for Spurs).
Both OGS and Emery have inherited teams from illustrious predecessors who probably hung on too long; in Emery's case, I have always thought that he would take at least two years - four transfer windows - at the minimum to get Arsenal where he would like to have the club. Given that Arsenal tend to prefer stability, I don't see Emery in danger this season, and - furthermore - some of Arsenal's better defensively minded players are still out injured from last season.
Re OGS, it will also take him at least two years to achieve something with Manchester United; as with Arsenal, the team is in a state of transition, but, unlike Arsenal - where, once the egregious elements of the defence have been attended to, you actually have the bones of a decent team, - Manchester United are still a group of disparate players - some gifted - who haven't found a way to play as a team with a common vision, and sense of purpose and common identity.