Is anyone a hero in King Lear?

Short answer? Eh. I mean could I overanalyze and force one or more of the characters to fit that description? Sure.
And that's exactly what I'm going to do.
To me, the only character who even slightly resembles a hero is Edgar. He follows a hero's journey fairly close. A case could also be made for Lear, but I don't think he quite reaches any Apotheosis or most of the steps.
Edgar, however, reaches most, if not all. While not all on stage, he still references some occurrences offstage.

1. Departure 
1. The Call to Adventure: Edgar is called to adventure as soon as we're introduced to him. He's forced from his home as Edmund betrays him and makes falsehoods about him to their father
2. Refusal of the Call: Naturally, Edgar doesn't want to leave. He is VERY confused and doesn't understand what's going on.
3. Supernatural Aid: There really isn't any obvious aid to him. The fact that he survives could be considered supernatural aid, but that's a stretch I don't think I have enough evidence to make.
4. Crossing the Threshold: Edgar crosses the threshold when he calls himself "Poor Tom." He takes on the façade of a beggar to live, and accepts the adventure.
5. Belly of the Whale: Edgar, by taking on the image of a beggar, must too, live like a beggar. 
2. Initiation 
1. The road of Trials: We can only assume Edgar faces his own trials while we don't see him. As a beggar, life has to be tough.
2. Meeting with the Goddess: King Lear  doesn't have too much supernatural in it, so there is not real meeting with goddesses either
3. Woman as a Temptress: Now I'm gonna take a step away from Edgar and go to Edmund. Edmund really faces 2 women as temptresses (Goneril and Regan) and takes his own (anti)hero's journey.
4. Atonement with the Father: Now this is one that is very obvious. Edgar does meet with Gloucester, and in a way atones for himself and his brother by helping Gloucester.
5. Apotheosis: Apotheosis is the ascension to godhood, the ultimate boon. For Edgar, his ultimate boon could be either meeting his father again, or killing his brother. 
3. Return
1. Refusal of the Return: Edgar really doesn't refuse any return, so this is not super applicable.
2. The Magic Flight: Again, doesn't really happen to him. Although his whole journey with Gloucester could be interpreted as a magic flight as it is him being reunited with his father.
3. Rescue from the Without: His rescue is from his beggar status. When Edgar reveals himself, he is treated with respect that he deserves.
4. The Crossing of the Return Threshold: This happens when he reveals himself, like in the last one.
5. Master of Two Worlds: Edgar is master of both the world of highborn and lowborn. After living with both, he knows both of their struggles.
6. Freedom to Live: Probably his biggest redeeming factor. Edgar is one of the only characters who lives throughout the end. His death is not foreshadowed, and he has status to potentially become king.

So is Edgar the hero? I would argue that yes, he could be. He follows the mono-myth very closely, and arguably the closest in the play. While not all are met, that seldom happens.