If you have a Button in your second DataList then you can do something like this (server-side approach):
protected void Button1_Click(object sender, EventArgs e)
{
Button btn = (Button)sender;
DataListItem item = (DataListItem)btn.NamingContainer;
if (item != null)
{
Label lbl = (Label)DataList1.Items[0].FindControl("YourLabelID");
lbl.Text = "Some text here";
}
}