Fun with Conan the Grammarian

Dear Conan,

If a two-word descriptive has a first word that ends in ly, isn’t the hyphen automatically eliminated?

Example: Selling privately owned businesses nationwide.

I remember this as an AP rule but do not know if it is a general grammar rule.

~Midge

This brings a tear of joy to my eye. Anyone who internalizes obscure grammar rules like the one above is a true hero of the people in my book. Keep up the good work.

Your ally in correctness,

Conan