I think that the similarities are these:
in Goodbyes and Grief in Real Time the man there was telling the social media about what was happening to his mother and how he started to tell it to social media as if to announce to the whole world. while in the Lottery, it also has the same way of announcing, only that it is not online. another similarity is that people are responding to what the person had said
They were held at different times.
The plot of the two stories are somewhat similar but not really the same(the deaths of Tessie Hutchinson in the Lottery, while the mother of the man in Goodbyes and Grief in Real Time)
that just sums up my answer hope it helps