In other words, it doesn't look like the lame.exe ever starts up

EAC spawns a CMD window (AKA DOS box!) with Lame running in it. If this indeed happened correctly you would certainly notice it, unless your taskbar is set to auto-hide and the CMD window was hidden behind something.
In all probability Lame never executes or if it does it's bombing straight away.
You should test Lame isn't corrupt: Open a CMD window where Lame lives and run it without parameters, you should get a screen of text with version no. and usage parameters.

I have just tried to fool EAC about where Lame lives and it returns "Wrong path or program!" - try doing the same as a sanity check.