As all other David lynch movies Eraserhead also is hard to grasp. I would like to understand what exactly the film suggests or explains. Particularly what is the significance of the "Lady in the Radiator".
The most widely accepted representation of the lady in the radiator is that she represents death.
The mysterious Lady in the Radiator (Laurel Near) represents the Grim Reaper and sings to Henry an eerie song of heaven and of how "everything is fine" there. It can be stated that the radiator itself is representative of Henry's thoughts of self-destruction and that he sees death as a source of freedom from his living Hell. This view seems to be confirmed at the film's shocking climax when Henry kills his baby in act of release and mercy. He is then met by the Lady in the Radiator in a brilliant flash of light and dies in her arms. In this act, Henry has finally embraced Death and accepted it into his life, giving him admittance to his own personal heaven and freedom.
Taken from http://notcoming.com/reviews/eraserhead/
This lady in the radiator is death. She intrigues Henry because she is a form of escape from his existence. To further secure this claim is her soothing anthem “in heaven everything is fine.”
As stated, the Lady in the Radiator represents death, but i believe it is not so much as an outside "grim repear" figure, but the personification and creation of Henry's imagination, representing his own suicidal thoughts that would allow him to escape his depressed and hellish life.
All throughout the movie we see Henry dealing with his own depression and being put in situations of high anxiety, so when he is alone in his bed, he imagines (maybe dreams after going to bed?), of this lady in the radiator, being an escape to his life, and so, Death.
But this death figure is not so dark as the Grim Reaper would be, instead, the death figure appears to be the only happy and somewhat comfortable place Henry can find, while at the same time being very eery, it plays a lot on the duality of death as seen by a suicidal person, for example,
The music, the melody and pace have a very calm and comforting tone to it, while at the same time has grim lyrics, stating that "in heaven everything is fine" (and so death would be better);
The lady, she presents herself as a very cute and charming character, while at the same time having some grotesque features and weird actions (like killing the babies that fell on stage), like Death is to Henry, a happy place that is also very dark;
The stage, very commonly used by David Lynch, a stage/curtains, often used to represent a place where reality and dream are mixed and unidentified, a place where a show should be held and something you would like to see is a scene for baby killings;
This duality plays in Henry internal monologue of seeing death as the only happy place he can go to, but at the same time fearing it.
So when Henry accepts death, i believe this represents his suicide, coming from within himself and the need to escape life, manifested in the form of this lady in the radiator, and so Henry dies in her arms, giving in to the personification of his suicidal thoughs.
The lady in the radiator represents acceptance of circumstance and self possession of state of mind. She is the symbiotic pair to the mutant baby which represents fear and fatalism. Notably, both the lady and the baby are physically projected by Henry as mushroom clouds through which the layers of dream logic the movie takes us. The unseen dreamer who's dreams we are seeing in the movie have intermingled his sexual and existential fears into both 'characters.' While the dreamer still lives with the threat of the mushroom cloud by choosing the lady over the baby, he accepts the reality of the situation over fear and denial, while simultaneously rejecting the fatalism of the dream image he observes of himself in Henry - He believes that he can control his own mindset and not be victim to primal instincts inherent in his own nature as a man