Question deals with the connotation and denotation of the author's words.
For the denotation of the words, all three--house, home and dwelling--have very similar meanings--they are places in which people live.
It is in the connotation--the way these words are used in common speech--that you can find the difference.
The words 'house' and 'home' imply family, decoration, warmth, safety and security. It implies personal touches and time spent on making the structure, the building, into someplace one would feel comfortable.
The word 'dwelling,' on the other hand, implies a physical structure only--four walls, a roof and a floor. To dwell is to live, but not necessarily to create a sense of warmth and security.
This fits with the impresonal setting that Lowry has created in her dystopic society.