You are iterating through the string "ID" as lb_Chosen.ValueMember is a string with value "ID".
You should use something like the code below to get your IDs:
for (int i = 0; i < lb_Chosen.Items.Count; i++)
{
MessageBox.Show((lb_Chosen.Items[i] as YourAccountClass).ID.ToString());
}
Edit: translated names in code to english