"Under the Lion's Paw" certainly reflects the themes of naturalist literature. It aims to be realistic, trying to reveal the reality of life within agricultural communities.This is shown even in the story's very first paragraphs, which provide a detailed, heavily visual description of farm work and farm life. It attempts to depict what agricultural life actually entails, rather than provide an idealized vision of that life.
Additionally, this story reflects some of the larger sociological and thematic concerns that Naturalism as a movement seems to reflect. Not only is agricultural life described in detail, these descriptions establish agriculture as hard, incredibly grueling work. In essence, "Under the Lion's Paw" establishes its characters living their lives at the mercy of nature, and moreover, as the story ultimately establishes, at the mercy of their landlords: people such as Butler. Greed and exploitation are key themes within this story, and Haskins is rendered helpless in the face of that exploitation.
Naturalism with regard to this story can be defined as the way in which Garland strove to depict the characters and the situation in this story to be as realistic as possible so that they matched real life, rather than being just an idealistic representation of reality. This is achieved through the description of the backbreaking and soul crushing work that is necessary to make a farm profitable. Note, for example, how the narrator describes the eldest son of Haskins:
An infinitely pathetic but common figure this boy on the American farm, where there is no law against child labor. To see him in his coarse clothing, his huge boots, and his ragged cap, as he staggered with a pail of water from the well, or trudged in the cold and cheerless dawn out into the frosty field behind his team, gave the city-bred visitor a sharp pang of sympathetic pain. Yet Haskins loved his boy, and would have saved him from this if he could, but he could not.
There is no romantic idealisation of farming and the kind of life that it is in this quote. Instead, making children work on farms is compared to "child labour" and visitors from the city are shown to have "a sharp pang of sympathetic pain" when they see Haskins' eldest boy working away on the farm. Even Haskins himself would have saved him from the fate of being an endless drudge if he could, but he was not able to. There is a sense in which both the boy and Haskins are presented as being trapped by the life of a farmer that Haskins has chosen for him and his family. Naturalism is also shown in the way that Butler callously and selfishly raises the price of the farm after the hard work that Haskins put into it. Note how the narrator says Butler raises the price in a "careless and decided voice." There is no jot of sympathy in Butler, and in his characterisation Garland captures the reality of so many materialistic and greedy land speculators, who deliberately profit out of other people's misery and need. The rage with which Haskins meets the announcement that the farm he has worked so hard on is going to profit Butler more than himself mirrors Garland's own feelings about the way farmers were treated and the raw deal they were so often given. Naturalism therefore is demonstrated in the real life description of what it takes to run a farm, and also the way in which farmers are treated.