lines 8-10 of The Lady or the Tiger What type of conflict is the accused experiencing at this point in the story? person vs. tradition person vs. society person vs. self person vs. nature

It is unclear what part of the story lines 8-10 refer to, but I will consider both lines 8-10 of the story as well as the first introduction of the accused later in the story.
"The Lady, or the Tiger?" opens with a description of the "semi-barbaric king" and his ritual of deciding the guilt or innocence of his subjects who've been accused of crimes. In the PDF version of the story I am reading, the king is described in lines 8-10:

but, whenever there was a little hitch, and some of his orbs got out of their orbits, he was blander and more genial still, for nothing pleased him so much as to make the crooked straight and crush down uneven places.

This section describes the king's demeanor and his desire to "make the crooked straight," which could refer to his sense of justice. This section of the story indicates that the king's main conflict is within himself (person vs. self) as he reconciles the different aspects of his "semi-barbaric" personality. However, the accused is not mentioned at this point of the story.
Later, a general "accused" is introduced into the story when the narrator describes the tradition of justice the king has continued. Basically, the person accused of the crime is made to enter an ampitheatre/arena and choose one of two doors. The narrator explains,

It was the duty and the privilege of the person on trial to walk directly to these doors and open one of them. He could open either door he pleased; he was subject to no guidance or influence but that of the aforementioned impartial and incorruptible chance.

Here, the narrator indicates that the ritual presents a conflict of person vs. self or person vs. tradition. The idea that the accused has "no guidance or influence" takes the society and the king himself out of the equation. The ritual is set up so that the accused imagines he can control his own fate. The two doors will reveal either a tiger, which will eat him, or a lady, who will marry him. Although the accused picks the door, the tradition dictates his options; thus, both conflicts are clearly seen here.
The particular accused of this story is the princess's lover, so the king is more personally invested in this case than he would be in a general trial. Of course the princess is invested, as well. The story never actually reveals the outcome of the trial, but in terms of the conflict presented, there is more of a person vs. person conflict here since the king has more interest in what happens to the accused. There is also a person vs. person conflict between the accused and his lover, since she gives him a hint to what door to choose (she knows which has the tiger and which the lady); however, we know she is jealous of the lady who was chosen, so we are left unsure which option she points him to. The person vs. tradition conflict persists, as well, since this is still the same ritual that is usually performed. The person vs. self conflict is less pronounced here since the accused looks to the princess for guidance.