Delta rep made a presentation at my work today. He said DL is looking to complete the move to T2 and T3 by Summer 2017, pending LA city council approval on renovation plan and compensation to other airlines, which Delta expects the city council will approve in May or June.
After that, there will be a phased-move with airlines moving one at a time from T2 to TBIT, and from T3 to T5 or T6 while Delta shifts some flight operations to T3, until all the flights are moved by Summer 2017. Renovation (probably just interim reno) of T3 will begin as soon as Delta has a lease on the terminal. A complete rebuild of T3 may have to wait until MSC is done so Delta can temporary use some TBIT North and/or TBIT MSC gates.
To facilitate transit to Virgin Atlantic and other SkyTeam partners prior to the rebuild, the plan is to have air-side bus connection between T2, T3, and TBIT until T3 rebuild is completed.