I was just able to download the Crimson map pack via the in-game store. I have the LE. Hope this helps.
I don’t have the LE but I bought the map pack, and I can also confirm I’m able to download it now.
Mmmhm. Read all about it here:
https://forums.halowaypoint.com/yaf_postst162869_Crimson-MP-Update-for-LE-and-Map-Pass-Owners.aspx