Is it legal for a Laboratory to withhold results from the ordering provider until a self pay patient pays their bill in full?
Depends on the contract
This entirely depends on the contract, and technically even if you ordered it or the doctor - who might have credit with the lab and bills you in return.
However, depending on the contract you might have agreed to payment being due before being allowed to get the result. Read the contract. It is relevant what is written there: who is the actual party to the contract and under what modalities do the results get to whom?
- If you ordered, you are entitled to the results under the contract with the lab.
- If the doc ordered, you are not entitled to results from the lab, the doctor is. You are entitled only to results from the doctor from your treatment contract with the doctor.
Do note, that in either case, when you are entitled to the results is spelled out there. It could be "Once available" or "Once paid" or even "by specified date".
Depending on the type of test done, there might or might not be an ethical problem:
There is nothing life-threatening in a paternity test, waiting for the results until the bill is paid wouldn't be at best distressing, but usually not in a manner that would be unethical.
An HIV-test or one for other STDs is quite life-changing, and not telling those results could endanger the person or their close kin. Not giving the results of such a life-changing test might be a breach of the duties of a medical service supplier. These however are spelled out by the relevant medical communities.