After some thought, I'd like to add Lewisham to my preferred list of Woking and Windmill Bridge.
Trying to look at it in terms of
Bald Rick's requirements...
To answer the OPs question precisely, ie ‘the most compelling case’ you will need to understand the benefits of such a flying junction.
Typically the most benefits arise from enabling additional trains to run. Journey time improvements and reliability gains help, but it is more capacity that wins the argument. Crucially that extra capacity has to be useable, ie there is spare capacity elsewhere on the network and the flying junction unlocks it. And, the more valuable each train path is the better, valuable being determined by number of passengers on the train and the likely average fare they pay.
So if capacity is key... Lewisham wouldn't allow more trains - that's constrained by capacity at the London terminals. But it would allow more trains to stop at Lewisham, which would have much the same impact in bringing in more passengers: Right now we have the absurd situation where about half of the metro services round Lewisham actually skip a key interchange station, running along the avoiding lines instead, in order to avoid too many conflicts on the flat junctions. That kills viability for a lot of potential interchange journeys: Stations along the Sidcup, Grove Park and Hayes lines onto the DLR and 'orbital' journeys around London that would involve interchanging between those lines at Lewisham. It also makes travelling
to Lewisham by train from a lot of outer London destinations less attractive. Solving those problems by infrastructure that enables all metro trains to stop at Lewisham would seem likely to bring many more passengers onto the existing metro trains on exactly the sections of their routes South/East of Lewisham where those trains are currently least busy. And that's even before we talk about the Bakerloo line extension.
(And it would help a lot on reliability too, though Bald Rick indicates that's not the thing that wins the argument).
Unfortunately the devil in this room is how/where you could get a flying junction that would help. You have about five flat junctions in succession around Lewisham, and almost no land nearby on which to build anything. Add to that the the single junction which I'm guessing is the one that causes the most problems is right at the end of the platforms. I imagine any solution is going to involve some tunnelling, so won't come cheap. And it's not obvious to me what the solution might look like.