Though Shaketeach is correct is connecting the characters that Shakespeare was writing to a pre-Christian Britain, it is also theatrically true that the world of the play (especially Shakespeare's plays) belongs to the time and place chosen for each particular production, and therefore are open to interpretation. This is always possible when considering a play, for, unlike a novel, it is not frozen in time and place. Even Shakespeare's players, in staging Julius Caesar, for example, wore modern Elizabethan dress, making no attempt to "set the play" in ancient Rome.
So, if we can assume that the world of King Lear is an issue to be decided by a director/theatre company producing the play, then we might find it more possible to look at the characters allegorically. Under these circumstances, we can find Christian symbolism. The idea of "penance" is worth considering in a Tragedy like King Lear, since the notion of serving penance for sinful deeds dovetails nicely with the path of a Tragic Hero -- one who must suffer the consequences of his tragic flaw.
And a strong case can be made for Lear, the Tragic Hero, spending the majority of the play on the heath doing penance for his past sin. If sin can be connected with his tragic flaw, this would be easily exhibited by Lear in the opening scene of the play when he favors flattery and adoration over humility and simple love. His sin/tragic flaw? Hubris or pride, which "goeth before a fall."
Much has also been made of the ending of the play as "redemptive" in a Christian sense and comparisons have been made between Cordelia and Christ. Your question is quite large, so you should investigate whichever of these paths interests you. The possibilities certainly exist.
I'm not sure what you mean when you say forces of evil and atheism. The story of the historical King Lear pre-dates Christ. The play is set in a pre-Christian world. If religion did play a part in the play, it would be Druid. Penance is also a Christian concept that would be alien in the world of the play.
It is true that Shakespeare wrote the play during a period when religion played a strong role in everyday Elizabethan life. There is however a difference between reality and the world of the play. When characters do speak of gods, they use a plural reference or in Edmond's case, he calls upon Nature as his goddess.
Do evil things happen in the play? They do. Are Goneril and Regan evil or are they trying to protect themselves against their father who has become a tyrant. (There are no easy answers in Shakespeare.) They had seen how easily he had disowned, Cordelia, his favorite and exiled Kent for his honesty. They had played daddy's game and lost. He was suppose to live full time with Cordelia. Now Lear would be under foot for long periods of time with all his men. If they did anything to displease him, what would the volatile old man do to them? Who of us wouldn't want to protect ourselves under these circumstances. Do they go too far? Of course they do. Once an action like this starts, it is like a snowball rolling down a hill, hard to stop.
More important thematically is how does one be a good king and a good father? At the beginning of the play, Lear is neither. He is a foolish old man who wants to be flattered and ego stroked. He doesn't know how to retire. Both Goneril and Regan understand and give him what he wants. Is this love? Since Lear doesn't know how to love or what is love for that matter, probably not but it passes for love in the Lear household. Do these two women love their father? In their own way they probably do but like many of the father/daughter relationships in Shakespeare, the fathers have difficulty expressing their love.
Does Cordelia know how to love? She does so that when asked how much she loves him she finds that she cannot find the words, "I cannot heave my heart into my mouth."
The storm scene is one of the most amazing scenes in the play as Lear goes mad and challenges the raging storm. Yes, he does mention sin but in the context of that world. It during this that for the first time, the old king thinks about somebody other than himself. He sees the suffering of the Fool. When he encounters poor Tom, he sees the "mad" Edger as a wise man. He strips off his clothing to discover that in the flesh, so to speak, we are all alike. "...man is no more but such a poor, bare, forked animal..." For the first time he understands suffering and the human condition.
When Lear and Cordelia are reunited, Cordelia's gentle love brings him back not only to consciousness but to sanity. Does the old king learn? Eventually, but their joy is short lived.
Is there a lesson here? There are many. The play is rich with ideas.
We cannot judge the world of the play by today's values and standards but we can accept it and learn from it.