Berthold

~~Moved to TOurist Visas, from K1 Progress Reports the OP is asking about visiting.~~

Even if the person passed away, lying in an immigration form can be deemed as material misrepresentation and the consequence is a ban, which can only be lifted (in some cases) with a waiver.

Embassies don’t look favorably on people lying to try get a visa, and this will be on her record. I’d keep expectations of getting a tourist visa low. 

Being completely honest is the right approach. She could try but like others have said, the chances of her getting a tourist visa are low 😞

If your current intentions are to only be able to visit the US for short spurts, then the tourist visa is your only option. But given her previous denials, it's probably unlikely she will get it this time around. The other thing to note is that you are 100% ineligible for the K-1 because you are already married. K-1 is ONLY for engaged couples, not married couples. Second important thing to note is that if you married in one country, then you are considered married everywhere. There is no need to get married again inside the USA. And please don't try to get married "again" in the USA because that will cause MAJOR problems in other legal aspects, not just with immigration. I don't know about Thailand specifically but it sounds like you need to register the marriage with the Thai government to get whatever official marriage certificate (or equivalent) they hand off to you as proof of your marriage. You will need that document for sure for whenever you DO decide to pursue the spousal visa (which only exists for the sole purpose of permanent residence in the USA). Hope that all makes sense.

Seems like some lying was involved. In any way visitor visa is the only visa she could try for now but based on your post, approval is u likely.
 
One note, not sure what sort of mess was involved, but if she had listed herself as married during any of those four visa applications, it will haunt her even when you two plan to immigrate in the future using spousal visa.

That sounds like the best way to approach her next interview for the tourist visa.
 
However, it's best to keep your expectations low. Four times denied is a lot.

Too married for a K-1.  Not married enough for a CR-1 
 
 
A k-1 is for people who are not married (she is too married) who plan to marry the US citizen petitioner within 90 days of entry to into the USA and then adjust status to an immigrant.  
 
A k-1 is not the correct visa.  
 
A B-2 or B-1/B-2 visa is the correct visa.  For all the reasons mentioned in your OP and by others she isn’t likely to get one.  
 
Given the difficulties of a Thai citizen getting a civil marriage certificate  to a non Thai (requires in convent of the non citizen’s embassy in Thailand and with Covid that embassy might have better things to do) I suggest doing the Utah zoom marriage so that from a US perspective there is no ambiguity as to her marital status. The bride, groom, and officiant do not have to be in Utah or the USA to do this. 
https://www.visajourney.com/forums/topic/751556-query-regarding-webwed-mobile-marriage-online/?do=findComment&comment=10316916
 
Of course if she falsely claimed to be married to someone else in the past, then it will be difficult for her to ever come to the USA until that person passes away.  
 
 

Thank you for your responses. Yes, it seems some lying was involved. I get the feeling her previous boyfriend suggested she pretend she just wanted to visit and to not admit she had a U.S. boyfriend. Then it seems an agency told her she should pretend she wanted to visit Chicago and gave her some sound bites to use in her interview. ("I want to see the Chicago music scene" and silly things like that.) She didn't suggest any previous marriage to immigration. So, I understand that it appears a tourist visa is the best or only option here? I suppose the best tack is to just be completely honest: I tried three or four other times but each time I followed the advice of less than reliable sources. I am now married to an American. We don't plan to move to the U.S. permanently for several years. I want to become fully vested in my retirement here in Thailand. But I want to visit Berthold's family and especially his mother who has COPD, some dementia, and a heart condition...." Does that sound right?
 
Thanks again and again for your help!