The fact that it was well-established long before op's 1930s movies is attested by this sentence in the transactions of the annual meeting from the south carolina bar association, 1886 and to. I had always understood 'there's no such thing as a free lunch' as a expression to demonstrate the economics concept of opportunity cost - whereby even if the lunch is fully paid for, one loses. Saying free or available rather than busy may be considered a more positive enquiry.
Understanding the Context
It may also simply mean that you expect the person to be busy rather than free, rather than the other way.
