I've never had a problem with Lucien and Shadowmere, but I did just have my first experience of Shadowmere simply vanishing. I have been in a hurry equipping the citizenry with new weapons, and I fast traveled to Skyhaven (on my way to Old Hroldan) just to check Delphine is still missing her Blades armour (she was

) and because I arrived inside Shadowmere was completely gone. I should have checked with the console just where he was, but I was in a hurry, and he did show up the next time I fast traveled.

If you're on PC there's commands for everything from going to him, bringing him to you, or making a copy of him. He often inexplicably runs off almost beyond my rendering distance in my game and then will just stand there forever (presumably) if I don't go fetch him. I always hunt for him with the Aura Whisper shout when this happens.
Edit: I'll be glad when I finally finish running all over Skyrim reverse pickpocketing the NPCs, and then Shadowmere can go back to just hanging out in the Riften stable.