Having Director of Football is one thing but having the Director of Football to be the one who picks and buys the players is silly because (a) having a Director of Football is not a foolproof approach, (b) what if the signings that the Director of Football make do not turn out great and (c) what if the manager does not like the players that the Director of Football bought? Then what?
Like it or not, there are always gonna be hits and misses when it comes to transfers and ideally, we would want to have more hits than misses. The key things are (a) the club have a clear idea what they want to be like, what kind of football do they want the team to play etc and (b) Director of Football or not, the manager and the board work closely with each other to identify the targets that the manager wants and is aligned with the club's overall strategy/plan for the playing team. Liverpool and Man City, for example, have their own Director of Football but they do not go and buy the players and just throw them onto Klopp and Guardiola. They work closely with them to get who they want.
The reasons why we have failed or have had mixed success with transfers in recent years are (a) the club have been yo-yo-ing between the kind of football they want the team to play and (b) recent managers were pain in the arse to work with. We had AVB and I guess to an extent RDM to introduce a more progressive playing style and move away from the pragmatic football. We even bought exciting young players like De Bruyne, Mata, Hazard, Oscar etc. But then after some bad results, the club reverted to type and went with pragmatic football and managers again - Benitez (albeit an interim manager), Mourinho and then Conte. And suddenly, the club decided to go for the progressive football and move away from the pragmatic style with Sarri and now Lampard. On top of that manager, those managers - Mourinho, Conte and Sarri - were also seemingly a pain to work with, one way or another. Mourinho and Conte threw their toys out of the pram immediately when they could not get their first choice targets and IIRC in Conte's case, he reportedly turned off his phone so that he could not be contacted by the board about transfers in the summer of 2017. As for Sarri, he was (still is I guess) a manager who doesn't fancy getting too much with all these transfer businesses.
Maybe this is still a bit early to form a definite conclusion about it but it finally looks like the club are getting their act together in terms of direction of the playing style and team and working with the manager to buy players. Lampard has constantly spoken about working closely with Marina, with Cech in the transfer market - as mentioned by other posters here, having Cech in the board does seem to have helped massively especially in bridging the gap between manager and board - and unlike previous managers, he does not moan and complain about the board in the media. He has always ensured that there is a positive working relationship between himself and the board. You might not be convinced about the signings of Werner, Havertz, Ziyech etc yet but I think overall, they have too much quality to be total flops for us. And it does seem clear that we want to play progressive football moving forward and so when we hire our next manager - whether because Lampard gets sacked, decides to move or for whatever reason - it is important then that we get a manager who has the same philosophy and progressive playing style to ensure the continuity. We can't just revert to type and hire another pragmatic manager again.