Polar express

It'll work fine on any O-gauge track, but the LC model must have it's remote.  If it's the new model with BlueTooth, you can also run it with the LC application on a smart device.

You can use any common model train transformer, and the LC products run on DC or AC.

LionChief engines depend on the remote to operate.

LionChief with Bluetooth engines can also be controlled using Lionel’s app.

LionChief Plus engines can be run conventionally through transformer control.

LionChief Plus with Bluetooth engines can be run conventionally through transformer control or via the app.

Assuming you are talking about the Polar Express starter set, it’s either LionChief or LionChief with Bluetooth. Use the product number to determine which set you have on Lionel’s website, if you don’t still have the box and instructions (which specify how the train is configured).

Dave

any transformer will work. You just need to put about 16-19 volts on the track. The signal from the remote to the engine will control speed. One thing to remember is that if you leave it sit on the track it has a “safety shutdown”. You’ll have to drop the voltage to 0 and bring it back up, to re-establish control. 
Marty

I have the PE 15 year anniversary set. I am running it on MTH Real Trax. I am using my post war Lionel SW transformer to power the track. Pretty simple to do. Set the voltage to around 18. The passenger cars light up and the train makes that noise waiting for you to turn on the remote. Turn on the remote and your in business. I can also use my Samsung tablet or Samsung phone with the Bluetooth.

The engine will not function using only the transformer. Thus you can not run it like a regular conventional engine. The transformer will only supply power to the track and the engine but no actual commands to the engine.

It would be the same procedure if you where using the old Lionel 027 track or Lionel Fast Track without the plug in wall wart power supply.