public class HistoryData
{
    public string GroupDate { get; set; }
    public List<Order> Orders { get; set; }
}

public class Order
{
    public OrderInfo OrderFullData { get; set; }
}

...
   var datas = resultData.OrdersInfoData
                                   .OrderBy(r => r.OrderNumber)
                                   .GroupBy(r => r.OrderDate)
                                   .ToDictionary(v => v.Key, v => v.Select(p => p))
                                   .ToList();
...

                        responseArchiveOrders.HistoryDatas = new List<HistoryData>();

                        foreach (KeyValuePair<DateTime, IEnumerable<OrderInfo>> item in datas)
                        {
                            HistoryData itemHistoryData = new HistoryData();

                            itemHistoryData.GroupDate = item.Key.ToString("yyyy-MM-dd");

                            itemHistoryData.Orders = new List<Order>();
                            foreach (var itemOrders in item.Value.ToList())
                            {
                                Order itemOrderData = new Order();
                                itemOrderData.OrderFullData = itemOrders;
                                itemHistoryData.Orders.Add(itemOrderData);
                            }

                            responseArchiveOrders.HistoryDatas.Add(itemHistoryData);
                        }	

                        d1.All(e =>
                        {
                            new HistoryData()
                            {
                                GroupDate = e.Key.ToString("yyyy-MM-dd"),
                                Orders = //??????? не могу написать заполнение без foreach
                            };
                            return true;
                        }
                        );	

                        responseArchiveOrders.HistoryDatas = d1.Keys.Select( k => new HistoryData()
                        {  
                            GroupDate = k.ToString("yyyy-MM-dd"),
                            Orders = d1.Values.Select(n => new Order()  { OrderFullData = n }).ToList()
                        });

                        responseArchiveOrders.HistoryDatas = d1.Select( k => new HistoryData()
                        {   GroupDate = k.Key.ToString("yyyy-MM-dd"),
                            Orders= k.Value.Select(n => new Order() { OrderFullData = n }).ToList()
                        }).ToList();