There are a few ironies in the story. In fact, these ironies are disturbing.
First, those who believe strongly in the lottery, do so with joy. They think that the lottery is something that should be celebrated, or something that people should look forward to, when in fact, it is a ritual of death. Here is a quote that shows the deep irony of this point.
The lottery was conducted--as were the square dances, the teen club, the Halloween program--by Mr. Summers. who had time and energy to devote to civic activities.
It should also be noted that Mr. Summers thought that stoning someone once a year was a civic activity.
Second, the whole concept of a lottery is ironic. This is probably the biggest irony in the story. A lottery suggests winning something. For example, people may say that they wish they could win the lottery. However in this case, the winning of the lottery is death by stoning. So, the very connotation of a lottery is turned upside down. Ironic.