I didn't see anyone answer this correctly. So I'm posting it here. In order to get columns to show up you need to specify the following line.
lvRegAnimals.View = View.Details;
And then add your columns after that.
lvRegAnimals.Columns.Add("Id", -2, HorizontalAlignment.Left);
lvRegAnimals.Columns.Add("Name", -2, HorizontalAlignment.Left);
lvRegAnimals.Columns.Add("Age", -2, HorizontalAlignment.Left);
Hope this helps anyone else looking for this answer in the future.