Determinism is defined as
the belief that all events are caused by things that happened before them and that people have no real ability to make choices or control what happens.
This philosophy suggests that man has no choice in his life but is instead controlled by the forces around him; it is generally seen as a helplessness at the hands of uncontrollable fate. Determinism is much like a naturalistic view, in which man is seen as being at the mercy of an uncontrollable nature. In Hamlin Garland's "Under the Lion's Paw," the Haskins are, as you suggest, victims of both natural and man-made determinism.
The Haskins are driven out of their Kansas home and their livelihood by a plague of grasshoppers "four years, hand runnin'"; this is obviously something which is far beyond their ability to predict, contain, or control. Despite all their hard work, they have to leave their home and land with virtually nothing because of elements beyond their control. Hamlin makes their plight clear:
There is no despair so deep as the despair of a homeless man or woman. To roam the roads of the country or the streets of the city, to feel there is no rood of ground on which the feet can rest, to halt weary and hungry outside lighted windows and hear laughter and song within, these are the hungers and rebellions that drive men to crime and women to shame.
To make matters worse, the Haskins actually traveled through this land in Indiana ("Ingyannie") where the Councils live and wanted to settle here but could not afford it when he and his family passed through four years ago. Things might have been different for the Haskins if they had been able to stay here.
Taking pity on them, Steve Council has determined to help this family get a fresh start.
"When I see a man down, an' things all on top of 'm, I jest like t' kick 'em off an' help 'm up. That's the kind of religion I got, an' it's about the only kind."
Now they are here and their fate seems to have changed. Council arranges for Haskins to lease a farm for three years; though the land and the house are dilapidated and the family literally has nothing, they are able to make a go of it. Council and others support his efforts, and the Haskins work unbelievably hard to make the farm successful.
No slave in the Roman galleys could have toiled so frightfully and lived, for this man thought himself a free man, and that he was working for his wife and babes.
For those three years, nature seems to have left the family alone, and, at the end of three years, the farm is thriving and prosperous. It is only a matter of time, however, before things which are out of their control once again determine their fate.
When Butler, the owner of the land, comes to see Haskins at the end of three years, Butler is impressed with all of the improvements which Haskins and his family were able to do on the land. He is unwilling, however, to give Haskins any credit, financially, for those improvements and unjustly (at least in Haskins's eyes) raises the price of the farm.
Once again, Haskins feels impotent in the face of things beyond his control (determinism). In his rage at the unfairness of Butler's actions, Haskins nearly kills Butler; he stops only when his your daughter appears. Resigned to the fact that he will have to pay twice for the land and house because his family needs a proper place to live, Haskins accepts Butler's deal.