It's not a lie (providing care for yourself), and your potential employer has no right to additional information as it relates to your medical condition and why you needed the time away from employment. Don't disclose what you don't have to. It provides you no benefit, and can only be used against you. Why would you sandbag your employer opportunities (and the ability to support yourself) because of faux moral hazard?
More importantly, why would one feel an employer is entitled to detailed information about this gap? It is none of their business.
It is a lie. You weren't providing care for a loved one (that's not how anyone would reasonably interpret 'love one'). It is indeed none of your employer's business. But still you should not deliberately mislead with an untruth.
Interviewers are only supposed to ask questions that are directly relevant to the job duties.
Whatever the reason for the job gap, there is no possible answer that is legally permissible. Remember more and more states are banning questions about jail time as well (look up 'ban the box'). So even if the person said, "I spent time in jail" that is still problematic. They may not have been convicted and considered innocent. Background checking services exist for a reason.
An interviewer asking about a job gap is already on sketchy legal ground.
The interviewer asking an inappropriate question is not entitled to a truthful answer to an inappropriate question that is not related to job qualifications.
Here is an example to help understand why this is problematic.
Lets say the candidate is religious.
They took a year off to go on a missionary trip.
If the candidate answers correctly (i.e. doesn't lie) the interviewer just discovered the candidate's religion.
This knowledge is now super problematic if the candidate is rejected.
This is why good interviewers do not ask about hobbies or what the person does outside of work hours. There is a real risk of discovering protected information (sexual orientation, religion, national origin, marital status, family situation - including plans to have children, etc.).
Remember a court of law is going to hear the question and the TMI answer that the candidate felt compelled to supply.
The intent of the interviewer will be determined by a court NOT the interviewer.
It is the truth that you are not required to disclose any information about medical situations of your own or your family, or any related to familial status, including even the fact that those issues exist or are medical in nature.
How else is one able to exercise their rights in circumstances like this without some mild obfuscation? "Providing care" is saying enough to signal that it is an issue which is likely medical in nature, without disclosing anything about your own medical condition or circumstances, which is your right. If your issue is only "for a loved one" then maybe you have a point, but you should have no issue with "I was a full-time care provider" and now we're just mincing words.
The goal is to explain enough to make it clear the question is related to medical conditions or familial status, so that the legally well-trained interviewer knows not to pry any further, and the interviewee who knows their rights has a perfectly good way to avoid discussing it any further if the interviewer asks for more information.
"I'd rather not discuss details about that, as the details are personal in nature and not in any way relevant here." That's all you should need to say.
I have seen situations evolve from privately disclosing some information about medical issues as a professional courtesy, into supervisor asking for updates as a logistical concern, and later unwanted discussion that continues as a matter of personal empathy, and then sometimes even more inappropriate discussions between parties that are not involved, or more public than you wanted; conversations that you wish wouldn't have ever started, over things that should have never even been an issue that needed to be discussed in the workplace.
My advice is to exercise your rights and avoid this as much as possible, which is to say, hopefully avoid it altogether.
More importantly, why would one feel an employer is entitled to detailed information about this gap? It is none of their business.