I'm trying to get my Mechanohog and I was wondering if it is possible to get into a heroic Lich King Dungeon if you're level 85.
It is. Simply right-click on your character portrait, and then change your dungeon difficulty (5 man) to heroic. When you enter a Wrath of the Lich King dungeon, it will be on heroic difficulty. Note that you'll have to physically enter the dungeon through the instance portal (which should have a skull in the display if you have the difficulty set to heroic).