For example, a millionaire forms an LLC to sell lemonade on the sidewalk and they put a job posting in the local newspaper where they specified that only a person of a particular ethnicity, marital status, and gender would be hired. He then rejected applicants accordingly.
The LLC has only a few planks of wood and a bag of lemons as its assets.
Is there anything that anyone could do legally to this millionaire?
The corporate veil can be pierced if the millionaire failed to sink in sufficient assets for the business to meet reasonably expected liabilities. In particular, the millionaire should have funded the LLC sufficient to hire qualified people and secure business liability insurance.
Further, anytime a corporate structure is set up specifically to be a liability shield and not with other reasonable reasons, it will generally be vacated by the courts. See Asset Protection by Atkisson & Riser, a must-read in this field. I know you are trying to create a "straw man" example for simplicity, but unfortunately the character and obvious purpose of the LLC does have a bearing on its survivability. Hardly anyone creates an LLC for a lemonade stand, which begs the question of "why do it".
It may be a defense against discrimination if the job listing was so particularly specific that the millionaire's child or ward was the only possible candidate, and then it could be defended as an educational exercise to show the ward how businesses are set up. Rather than an attempt to discriminate in any disallowed way.
