The London really isn't as good compared to 2.c4...(Yea yea yea I know some ppl are going to say Kamsky uses it blah blah blah but hes Kamsky and he plays stuff like the Ruy too so...)
Just go ahead and play 4...d6, 5...0-0 or 4...0-0 5...d6, it don't think it really matters. The KID setup is effective against the London btw. I guess you could play Nbd7 , but Im clinging towards Nc6 for some reason lol (maybe to route to the kingside I guess with Ne7). Aim for the e5 and f5 pushes I would say.
Don't forget, that with the absence of white's dark squared bishop on c1, a1-h8 diagonal gets weak and you might be able to plan an eventualy Nh5 to kick white's dark square bishop from defending e5, and then follow with a quick f5 after e5 (assuming white plays d5 in response to e5).
This is just my intuitive thought about the middlegame positions and I haven't really done any extensive analysis though so there might be something wrong with this line of thought and feel free to point it out :)
I believe this is called the London system
Because I almost exclusively play Nf6 against d4, white's absolute control of e5 becomes a problem because it makes it difficult to make a e4 pawn push....
I'm sure both Bg7 and d6 (the best 2 moves as far as I can tell) are more than sufficient, so I suppose what I'm asking is what sort of middle game motifs should I be looking for and what squares will be important? Should I ignore e5?