While this is a rather odd pair of stories to compare, there is, perhaps, a connection in the sense that the protagonists of the two accept happiness as dependent upon external conditions. For instance, Madame Loisel, who
grieved incessantly, feeling that she had been born for all the little niceties and luxuries of life
feels happy only when she is dressed well and "drunk with pleasure" in
a happy cloud composed of all the adulation, of all the admiring glances....
Likewise, the residents of Omelas are only content because of one poor creature who bears the misery of the community. Thus, happiness for both Mme. Loisel and those in Omelas is not genuine, for it does not come from within their hearts. Those who are disturbed by this knowledge and seek real contentment leave Omelas, but some do not understand and remain; likewise, Mathilde Loisel fails to realize that happiness does not emanate from luxuries, adulation, or admiring glances.
Therefore, in composing a thesis statement, the student may wish to draw the parrallels between the two stories. That is, in both "The Necklace" and "The Ones Who Walk Away from Omelas," there is a perception of happiness as a condition that depends upon the existence of others who are in a subservient condition, a condition external to the person, and a condition that is yet unrewarding because it is false.