using(SPSite site = new SPSite("https://yourspsite"))
{
    using(SPWeb web = site.OpenWeb())
    {
        SPList listA = web.Lists["listA"];
        SPList listB = web.Lists["listB"];

        // Assuming list A users are unique (based on your requirement)
        SPListItemCollection usersOnListA = listA.GetItems();
        SPListItemCollection usersOnListB;
        SPQuery query = new SPQuery();
        query.RowLimit = 1
        foreach(SPListItem userListA in usersOnListA)
        {
            // Get user on list B whose name is equal to user on list A, ordered descending by its date
            query.Query = @"<Where>
                               <Eq>
                                   <FieldRef Name='Employee_x0020_Name' />
                                   <Value Type='Text'>"+ userListA["Emplloyee_x0020_Name"].ToString() +@"</Value>
                               </Eq>
                          </Where>
                          <OrderBy>
                              <FieldRef Name='Date' Ascending='FALSE' />
                          </OrderBy>";
            usersOnListB = listB.GetItems(query);
            if(usersOnListB != null && usersOnListB.Count > 0)
            {
                // update date column in listA
                userListA["Date"] = DateTime.Parse(usersOnListB[0]["Date"].ToString());
                userListA.Update();
            }
        }
    }
}