private void Form1_Load(object sender, EventArgs e)
{
  this.dataContext = new DataContext("Connectionstring");

  Table<Contact> allContacts = dataContext.GetTable<Contact>();

  var contacts =
     from contact in allContacts
     select contact;

  this.dataGridView1.DataSource = contacts;

  this.ready = true;
}

private void dataGridView1_RowLeave(object sender, DataGridViewCellEventArgs e)
{
  if (!ready)
  return;

  dataContext.SubmitChanges();
}