In terms of the characteristics that are similar between the writing of Charles Dickens and D.H. Lawrence, one thing that both men seem to have had in common was their realistic portrayal of characters and circumstances, in their stories.
D.H. Lawrence's later work, when he moved to writing short fiction was characterized as exhibiting...
...the heightened realism of Henry James, Joseph Conrad, and Leo Tolstoy.
In "The Rocking-horse Winner," D.H. Lawrence delivers a convincing story of a boy who becomes obsessed with making money to match his mother's obsession to have money.
At last the mother said: "I will see if I can't make something." But she did not know where to begin. She racked her brains, and tried this thing and the other, but could not find anything successful. The failure made deep lines come into her face. Her children were growing up, they would have to go to school. There must be more money...
And so the house came to be haunted by the unspoken phrase: There must be more money! There must be more money!
Beside writing with marked realism, D.H. Lawrence's work reflected concerns over money, coming from a home where money was a greater worry than for others.
Lawrence’s childhood was marked by poverty and family discord.
Charles Dickens also wrote with a strong sense of realism. He had a photographic memory and based characters on people he met or people he was very close to.
For a time, Dickens rented a room with Elizabeth Roylance who was a friend of the family (when he father was sent to debtor's prison). He used Mrs. Roylance in as "Mrs. Pipchin" Dombey and Son.
..."[A] reduced old lady, long known to our family"... Dickens later immortalised [her]..."with a few alterations and embellishments."
Dickens had to go to work to pay for his family's debts (to get—ultimately—his entire family out of jail, so he worked in a factory gluing labels on jars of black shoe polish. He worked under harsh circumstances. When Dickens wrote David Copperfield, he included autobiographical information about the plight of the poor, forced to work for horrible wages in equally terrible circumstances.
Resentment stemming from his situation and the conditions under which working-class people lived became major themes of his works.
In reading David Copperfield, one can spot the spark of realism:
I thought of the oddest things. Of the shape of the room, of the cracks in the ceiling, of the paper on the walls, of the flaws in the window-glass making ripples and dimples on the prospect, of the washing-stand being rickety on its three legs, and having a discontented something about it, which reminded me of Mrs. Gummidge...
Interestingly, whereas both men came from poor backgrounds, their personal responses to such difficulties were very different. Lawrence had to work hard for acceptance, as many of his works (and behaviors) were deemed "socially unsuitable." D.H. Lawrence became cynical.
However, Dickens was very busy not just with writing, but in trying to better the world for those forced to work. He adopted a much more philanthropic outlook on life.
Each wrote with attention to detail to create a sense of realism in their work, however their works were extremely different in subject matter and plot development.