Does the donor of a gift exceeding the 2024 $18,000 annual exclusion have to pay taxes on the amount exceeding the annual exclusion if less than the donor's lifetime cap?

No, the donor doesn't have to pay taxes if they haven't reached the lifetime exemption, but they do need to file a gift tax return. What you need to file is: Form 709: US Gift (and Generation-Skipping Transfer) Tax Return. Keep in mind, married couples can double the $18,000 and count the gift as a joint gift.

Here is an article you may find helpful: The Gift Tax Made Simple

Thank you!  The article is helpful.  I filled out Form 709 and it's confusing because under Part II, Tax Computation, line 19 shows a "balance due" amount of approx. $24,000.  This is the first and only time I've filed a Gift Tax Return, so because I'm nowhere near the $13 million limit, I guess this amount is just charged against my limit and I am not obligated to pay taxes on that amount.  Is that correct?  I will not receive a tax bill from the IRS?

Following up on my reply to my question above??

You will not receive a tax bill for this, it is simply recorded to be tallied up with other amounts toward your unified credit limit.  

Thank you very much!!