Film a 3D video using Genlock cameras or LANC? I am doing some research in 3D stereo, particularly in 3D videos. I was successful creating 3D photos (using ordinary webcams) and viewing on a 3D laptop and 3D TV, but I've been reading that video recording is not so straightforward. 

What would be the cheapest way to build a 3D video camera set-up (Rigs, controllers, etc)? I live in India, so buying an expensive rig from abroad may not be possible at the moment. I'm also confused about using genlock cameras or a LANC controller for the video cameras. I currently don't have any video cameras, so which brands would be best to buy to have them in sync? My ultimate goal would be to film a scene 'live' in 3D (under 20 min).

Any help here would be very much appreciated.
Genlock would allow the capture of frames to be synchronized to a common external timecode.  It is only a feature on pretty high end cameras, so if you are trying to keep costs down, it really isn't an option.  The other question I linked to in the comment goes over a few possible ways to try to get usable sync for multiple cameras, but sadly, there aren't particularly good options for most cases.

There is a 3d kit for certain model GoPros that may be worth considering, but otherwise, you are probably best looking for a camera that supports lens splitting for 3d capture or purpose built consumer targeted cameras if you want things to remain fairly cheap.