Anyone know where the abandoned lodge key is? The lodge itself is southwest of Frostmoon Crag.

It's part of a side quest in Skaal village.
I believe talking to Deor is how you start it. Eventually, you will find the key and the quest will take you to the lodge.

Since it starts in Skaal, you need to be far enough in the main quest to start it.

I have completed the main quest and I have spoken with Deor repeatedly (he's not terribly deep) and no one's giving me the dialoge to start the quest.

Maybe you have to hear the argument about Baldor the smith being missing? I think you would have to have the quest Ask Deor about Baldor's Disappearance active in order to get any extra dialogue out of Doer. If the blacksmith is missing and you missed the argument maybe talking to the other villagers will bring up something about a missing smith.

If it is coded to start anything like the Blood on the Ice quest, I got the quest on my third or fourth visit to the village.

You can also talk to the barkeep in the Retching Netch; ask him about any rumors and he will tell you about the missing blacksmith. That should start the quest.