Richmond is one of those stations with an interesting history...
When I was little, so a a good few years ago (1960s), there was a barrier at platform/concourse level between the main terminating platforms (4-7, used (as the Ticket Office said) by LMS and LPTB District line trains), and the up Windsor line platform (2), also (terminating, bay) platform 3, the other side of its island: if you wanted to to change between the Windsor and Gunnersbury lines, you had to go up to bridge/booking hall level. Whether platform 3 at that stage was electrified I cannot recall (if I even noticed); as I recall, it was very little used, except for parking the occasional van. My recollection was that - almost invariably - LT District trains used platforms 6 & 7, 'LMS' NLL trains 4 & 5: at that time both used 3rd & 4th rail electrification. The double track, but little used, connection east of the station was not electrified: I believe when (after the North Western electric changed to 3rd rail only) a Southern 4-COR used it for a railtour, it coasted across.
I believe the double track Windsor-Gunnersbury connection was removed as part of the Feltham resignalling project, after which I don't think there was any connection: when (in Network South East days?) it was decided to use SR 2-EPB units on the NLL, a connection (electrified) was put in, trailing from the up Windsor line to platform 3, for stock transfer (the units were based at Selhurst). I think it was about that time that the barrier mentioned above was removed, and Richmond station was integrated.
Prior to about 1936 the Windsor line plaforms (1 & 2) were in what was essentially a separate station, a bit further west: when the Southern rebuilt the station 'as one' they do did so providing for quadrupling of the Windsor line: platform 3 would have become a through platform 'Up Windsor Local', while platform 1 would have become an island, with a new 'Down Local' line - I don't know how definite the quadrupling proposal for this was, but I believe the Twickenham Station rebuilding also took account of it.
Going way back (to Edwardian times, or even earlier), I don't know what the arrangements/agreements regarding the terminating platforms were: it may be that platforms 6 & 7 (using modern numbers) were the MDR's, and that originally (for their electrification in 1905) they were the only platforms done; with more (4 & 5) for the LNWR (NLL) electrification in c1916.