Has it ever been clarified or a approximate of how many members are in the Brotherhood of Steel including west and east coast also the Brotherhood Outcast since their still technically BOS members.

I don't think its ever been explicity stated.... The (W) BOS started from the troops assigned to the Mariposa Military base, and didn't really have a recruitment drive, and in FO1 seemed a small group, loving the warrior elite vibe. The MidWest BOS, although a splinter faction seemed bigger (to me at least) than the BOS in Fo1, however they agressively recruited.

http://fallout.wikia.com/wiki/Brotherhood

I also wouldnt describe the Outcasts as technically members. They've been exiled and their names stricken from the record.

Yea according to Elder Lyons and BOS members they've been exiled but they did say their trying to reconnect with the west coast possibly cause they haven't been completely kicked out of the BOS

Elder Lyons notes that the Brotherhood can barely keep the Citadel fortified. And since only small parts of the former Pentagon is in use, I'd say the Capital Wasteland BoS numbers around 100 soldiers, with Outcasts having less than 40 at their disposal.

because they want the WBOS to overturn Lyons, reinstate them, and put Lyons in his place.

This is something that continue's to intrigue me, I would estimate 150-200 soldiers for the capital wasteland BoS, not sure about the Outcasts. I always wondered why they couldn't come to some truce and let the Outcasts focus on Technology collection, and the BoS on maintained some order in the wastes, but do it under one banner.