Hello,
The lock-up is a function of the torque converter that allows the transmission to be coupled with the engine, reducing slippage, and increasing power availability and fuel mileage.
When the torque converter is locked up, but the wheels are not turning, the torque converter will not allow the engine to run.
The reason I do not think you have an issue with the torque converter, is that the torque converter does not care if you are in reverse or drive, it will stay locked when told to by the lock-up solenoid.
There are multiple possibilities, and some of them, like motor mounts, aren't even related to the transmission.
It needs to be scanned by professional equipment in order to understand what is happening. Once the problem is understood, the solution will be flushed out through testing of suspected components/systems.
I know there is a stigma about the cost of diagnostics, but the industry is changing, and more advanced diagnostic tools cut down repair time.
If you have other questions, or need more information, let me know, otherwise, here is a list of certified shops in your area with the training to repair your vehicle:http://repairpal.com/toyota-within-10-miles-of-new-waverly-texas-77358
