This sounds like a special situation in which your Lions Club should be represented by both an Ohio health care law attorney but also by a lawyer specializing in representing non-profits ... and you should pay them so the situation is covered by the attorneys' malpractice insurance in case any serious issues arise that result in litigation. Ohio has a pretty decent statute protecting volunteers, but I'm not certain the protections extend to entities such as your club.
The standard form Ohio Durable Power of Attorney for Health Care is designed to be signed by adults, and gives the individual Agent very, very broad authority to make virtually all medical decisions for the principal that the principal could make for himself/herself if able. The form even includes a nomination for the Agent to be appointed "Guardian of the Person" by a probate court if the need arises. It is my view that the standard Ohio medical power of attorney form is not suitable for what your club is doing ... that you need much more to define the limits of your responsibilities and to protect your club and yourselves.
I suspect that there are organizations, including your international, that have experience in doing what you are doing and have already dealt with these issues and have resources available so you do not need to reinvent the wheel and incur thousands of dollars of legal fees to do the good work you seek to do. You may wish to start with Nationwide Childrens Hospital in Columbus, which has treated many foreign children, to see if they can point you in the right direction. I would be glad to help you find some sources at Childrens or elsewhere (at no cost) but because we are swamped with year-end tax work I cannot devote any time to that project until after December 31.
Your Lions Club is to be commended for the Christmas blessing you are seeking to bestow on this child, but the legal issues surrounding your effort are complex and important. Don't do this without making sure you have covered all the liability issues.
Mr. Huddleston is an Ohio-Certified Specialist in Estate Planning, Trust & Probate Law, with offices in Columbus and Dayton, serving client families and private business owners throughout Ohio. He may be contacted directly by phone toll-free at 888.488.7878 or by email CLH@HUDDLAW.COM. Mr. Huddleston responds to Avvo questions as a public service to help educate and provide general guidance to questioners, but his responses are not legal advice and do not create an attorney-client relationship.