There are several types of remote control systems. Lionel uses three that I know of of which your grandson's is probably an IR line of sight type. The MTH uses at least two: one is the same IR system Lionel use and the other is MTH's own DCS control system which will not control Lionel trains that use theLionel digital control systems. I believe both Lionel and MTH trains will work on the old fashion transformer connected to the track.
The MTH DSC system requires the TIU box for trains and a separate AIU box for accessories. This is all very expensive. It kind of makes you select one or the other. But there are ways to run both the transformer and the DCS from a TIU (its complicated). You can even use Lionel digital control system on the same track as MTH's DCS but then you have to buy two control system that are pretty expensive.
LDBennett
