If the engine is running, you need to first step on the brake pedal, then engage the parking brake lever . . . I have a later model JD, but I think most operate this way.

Cut + Paste text from the attached link:

Using Park Brake

Locking park brake:

1. Push and hold brake pedal (A) down.

2. Pull park brake lever (B) up to lock park brake.

3. Release brake pedal. Pedal should stay down and park brake lever should stay locked.

Unlocking park brake:
1. Push and hold brake pedal down.

2. Push park brake lever down to unlock park brake.

3. Release brake pedal.

Here is a link that might be useful: Click on the left side menu: Using Parking Brake

This is what is in my LT155 manual. However I can sit on the tractor in the garage and put the brake down lift on the parking bread lever, and lock it. I can do this for "hours".

The problem is that when I leave the garage and get into the yard and try the same thing the the parking brake will not move.

I noted in archdiver post the comment about "the motor running."
Does anyone know if there is an interlock switch on the parking brake that would prevent it from being set when the engine is running? (2000 LT155 John Deere)

Does any one know of where I could get a diagram of the interlock switches?

You wouldn't be dealing w/ an interlock function. More likely a tension setting on the brake. Best to remove the deck and have a look at the brake tension and the P brake mechanism.