How to update lookup column through LINQ in SharePoint 2010

To update lookup field through LINQ, there is a tricky issue: we need to update "Display" column instead of "ID".

Below is the sample code.  The column "Animal" is a lookup column.

                using (ServerDataContext ctx = new ServerDataContext(strSiteUrl))
                {
                    EntityList<TestList1Item> Customers = ctx.GetList<TestList1Item>("testList1");
                    var query = from c in Customers.ToList()
                                select c;
                    foreach (var cust in query)
                    {
                        //cust.Animal.Id = 2;
                        cust.Animal.Title = "Dog";
                    }
                    ctx.SubmitChanges();
                }