transformer/plug for Legacy Base

Since Lionel has been providing warranty repairs on all the Legacy systems right now, why not contact them and ask, you may get a replacement for free.

As with the older TMCC system, the Legacy transformer and cord are special because one side of the transformer's secondary winding is connected to the grounding pin on the AC plug.  This connection carries an important component of the TMCC/Legacy signal to the track and locomotives.  If you try to use any standard off-the-shelf unit, it will not have this connection and will not work!  Get a Lionel unit.

There are no non-lionel substitutes for the plug

why do you need a second cord?

I own one Legacy base/remote.  I have a layout at home and I also have a fast track loop at my school.  I have found that playing with trains is a powerful motivator for my students!  Plus, selfishly, I get the biggest kick watching them play!  (I am continually amazed at how quickly they figure out how to use the legacy remote.)  So, when a kiddo earns it via a contract or when a classroom does something great I let them run an engine around the loop.  I bring my legacy base to work.  I want a second chord because to plug it into the wall I have to crawl under the table.  So, I am basically being lazy and just want to plug the base into the pigtailed chord.  I could use an extension chord, but then I still have to unplug it from my home layout.  At home I would like to have the chord wire stapled-neat and tidy!  Anyway, long winded explanation for convenience.

Well, I'd personally buy the Lionel brick.  If you're really wanting to "roll your own", the main feature is the outlet ground wire connected to one side of the secondary.  It's obviously possible to make this connection with a 3rd party transformer, just not as tidy.