Login to your account on store.stardock.com if you are entiled to a discount it will be there. It may seem like the same game with new paint but it's pretty awesome paint. 

LH is steam only I think. Unless that is for the free versions (I bought the game on preorder) I'm pretty sure the map pack will transfer in otherwise contact Stardock to see if it's compatbile. Otherwise just keep FE installed if you want to play on those maps. I still play WOM from time to time. More to compare where it started to where it is now and it still had mechanics that I'd like to see back in LH. Dynasties and armies limited by the max pop of your empire (I donno why I really liked this mechanic)

Can a Stardock guy clear this confusion for me?

The discount used to be available via steam, now it's only via Stardock. Will my steam-bought map DLC function with a Stardock-bought LH?

I'm not sure why you need Stardock to confirm something that you can confirm relatively quickly. On my account my Steam License is on the Stardock website. I entered the License into steam and now I download through Steam. If you want confirmation thats how this works search the site for Steam. Stardock is using steam to distribute content in such. Because of their coupon obligations they are doing the special keys on Stardock.com