If you do fall into a category where the IRS may not require a number, it's a situation where you will likely need to print the return and mail it. I would advise you to do that. There is no override I am aware of. It's also unusual for an accredited school not to have an EIN or refuse to provide one. They do know the IRS requirements.
I would reiterate the statement provided by @DaveF1006: You generally do not need an Employer Identification Number (EIN) for an educational institution when claiming the Lifetime Learning Credit (LLC) if the school is foreign and not required to have one, or if you can otherwise substantiate qualified expenses. However, the institution must still be an eligible educational institution.
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