Baby oil is quite a bit more expensive than sewing machine oil, and is not made to protect metal.

20 fl oz of Johnson's baby oil on Amazon is over $15.00.
32 fl oz of Sew-Rite sewing machine oil is $9.95.

Some mineral oils are as low as i $4.00 for 16 oz, so a little cheaper than sewing machine oil, but neither mineral oil or baby oil are formulated for protecting metal, as sewing machine oil is.