Probably many people will have a different opinion from mine, but I find Tessie's killing to be reasonable and fair for one particular reason. However, reading the story in its entirety, there is a good case to be made for a characterization of her death as unreasonable and unfair or reasonable and fair. You can decide for yourself after reading my response and doing some thinking about this.
First, Tessie is the most unlikable character in the entire story, in my opinion, because she is willing to put her daughter at risk to save herself. The way the lottery is set up, a slip of paper is drawn to choose the family. Then from the family members' names, the "winner" is chosen. When the Hutchinson family slip is drawn, Tessie starts to argue that her daughter should be included as part of the Hutchinson family, although she knows perfectly well that married daughters are part of a separate household for the purpose of the lottery. Including the daughter would decrease the odds of Tessie being selected. Thus, her daughter has escaped death for this drawing, but Tessie is arguing that she should be at risk, too. I find this to be odious and unnatural, and for that reason, it seems fair and reasonable that Tessie should be the victim.
Tessie's death, it can also be argued, is unreasonable and unfair because the death of anyone in the village would be unreasonable and unfair. There is nothing reasonable or fair about sacrificing one person a year under any circumstances. While there is dialogue in the story that speculates about the reason for the lottery, it is clear in the story that the lottery goes forward without any justification. It happens simply because it always has happened.
On the other hand, the lottery seems to be conducted quite fairly, everyone subject to the same set of rules and conditions. So, whoever is chosen has been chosen fairly. This is simply the luck of the draw. There are always winners and losers in a lottery of any sort, so in the "world" of this story, it would be as fair and reasonable for Tessie to die as it would be for anyone else.
How we read a story often depends a great deal on our point of view, and this is something that each of us must decide for ourselves. What I love about this story is how it stirs people up to start thinking about the issues it raises.