What lag bolts to use when mounting 65" TV to drywall using plywood?
The plywood plan sounds fine.  

The lag bolts through the plywood into the studs need to be long enough to go through the plywood, through the drywall, and engage about 1-1/4" to 1-1/2" into the stud proper - not any further or you risk hitting electrical gear.  For best results, pre-drill a hole into the stud somewhat smaller than the minor diameter (all-solid diameter) of the lag bolt.  

It would also help to drill the plywood out to the major diameter (edge of thread) of the lag bolts.  You don't want the threads engaging to the plywood, but rather, the stud.  Worst case if the threads engage the plywood, it can end up causing the plywood to push away and then stand off from the wall, putting the screw entirely in shear, not its best strength. You want the plywood to be somewhat in compression against the drywall, the drywall's best strength (and tension is the screw's best strength).

The screws from the TV mount into the plywood need to engage into the plywood, all else is wasted. Since you will only have 3/4" of engagement, use lots of extra screws.  They should also be snug.