The setting in "The Lottery Ticket" is the modest home of a middle class family. This is stated in the first sentence:
Ivan Dmitritch, a middle class man who lived with his family on an income of twelve hundred a year and was very well satisfied with his lot, sat down on the sofa after supper and began reading the newspaper.
The setting of a modest, middle class family home is important because it gives the reader a sense that this family is comfortable but certainly not rich. When the prospect of having a winning lottery ticket becomes apparent to Ivan and his wife, they forget how comfortable and satisfied they had been. They begin to daydream about the possibility of winning a fortune. In the process of that daydreaming, they come to resent each other and anyone else who might stand in the way of how they might spend the winning money. The setting is important. Had they been a rich, upper class family, the prospect of a winning lottery ticket would not be that exciting. If they had been dirt poor, it is more likely they would not become resentful in any way about winning since they had nothing to begin with.
In "Lucero," the setting is even more important, externally/physically speaking, but plays a similar role in determining how the protagonist will have to react. When Ruben Olmos meets another traveler on a path in which only one horse may pass, he is faced with deciding his fate on a 50/50 chance of guessing the face of a coin. Having lost, he is forced to push Lucero over the side. The setting, literally and physically, creates the possibility of such an all or nothing decision.
In "The Lottery Ticket," the setting of a middle class family determines how Ivan and his wife react internally to the possibility of winning the lottery. In "Lucero," the setting of the one-way mountain pass determines how Ruben must react externally. This is the big difference; internal conflicts versus external, and these frames begin with the setting. However, Ruben is clearly affected internally as he must sacrifice Lucero after losing the chance with the coin. Note that, to keep Lucero calm, Ruben kept his agony to himself:
Only then Ruben Olmos, his heart dissolved in agony, lightly patted Lucero's neck once more, and with an immense shove, sent him rolling into the abyss.
In each story, the setting plays a role in how the characters will/must react to a situation: moving from middle class to upper class and dealing with an impassible situation. In other words, the setting in each story plays a role in setting up how the conflict will arise. A middle class family will react to the potential winning lottery ticket differently than a poor family would. The one-way mountain pass creates the possibility of a conflict if Ruben were to meet another traveler. In "The Lottery Ticket," the setting leads mostly to internal conflicts with Ivan and his wife. In "Lucero," the setting leads first to the external conflict of two travelers trying to pass; it then leads to Ruben's internal conflict of sacrificing Lucero.