So I should state right away that I do not believe Lemongate. In my mind The House with the Red Door and a lemon tree is a faulty memory and a mashup of various places Dany has lived. In the end it will be a fictitious place that she can never really go back to. This will come into play in Winds because when she arrives in Westeros she’ll question if it’s truly home because it doesn’t feel like it. However she can never really return home because “home”, i.e. THWTRD, doesn’t exist as a specific place.
However many people instead think this is setting up some kind of reveal that Dany’s past is wrong in some way that’s not explained by a faulty memory. From what I can tell there are two main variations of this theory. Variation 1 is that Dany and Viserys spent some time in Dorne before fleeing to Essos and these are memories of her time there. Variation 2 is that “Dany” is not Daenerys daughter of Aerys but some other girl. Typically this theory is combined with her being the Tower of Joy baby and Jon Snow’s mother being Ashara. Personally I think both theories have issues that make them being true virtually impossible. However, I’m curious if anyone can provide evidence or an explanation for these inconsistencies.
Let’s start with variation 1. So we have Viserys and Dany spending time in Dorne(or maybe Dany alone but I fail to see why Viserys would let her be separated from him). Right away this begs the obvious question of “Why did they ever leave?” Doran had a marriage pact between Arianne and Viserys made with the Sealord of Braavos as witness. If this has been his plan for years why not keep Dany and Viserys in Dorne in secret? Why ship them off to Essos? By all accounts their lives were miserable with them constantly moving around and Viserys even having to sell his crown. If they were safely in Dorne they could have just stayed and Viserys would marry Arianne when the time came. Moreover why did the Sealord witness it? The obvious reason is that they were staying in Braavos at the time. But if they were in Dorne why not do it there? Did the Sea Lord happen to be in Dorne for some unrelated reason? Surely he didn’t sail all the way there just to be a glorified notary.
Variation 2 explains some of these issues but introduces new issues that, in my opinion, make it even more implausible. It also doesn’t answer the biggest question “Why send her to Essos at all?” For the moment, let’s say Dany is just someone entirely unrelated to the Targaryen’s. Maybe a Dayne bastard or something that looks more Targaryen. If this is the case then why is she able to ride dragons? The Daynes are First Men and even if she was somehow Valyrian, perhaps a dragon seed, how did the Dornish become aware of this? Did they just get lucky that their fake Targaryen has real ancestry?
Now let’s say she’s the daughter of Rhaegar. Right away we have to address the fact that this makes her the daughter of Lyanna and it means Ned willingly abandoned his niece to a foreign land and then did nothing when he discovered she was a beggar in Essos. I’m sorry but I just find this unbelievable. Surely he wanted to protect her enough to do something. Moreover if this theory is true it’s likely Jon is Ashara’s child. Ashara Dayne has features similar to a Valyrian even if she herself is not one. Why not just pass Lyanna’s child off as his own and raise Jon and “Dany” as twins? People would talk but it’s certainly a better life for her and I doubt people like Robert would question if she’s Targaryen when Dayne is the more obvious choice.
Even if we make allowances for why Ned was willing to leave her with others we have another problem. Why is “Dany” able to pass herself off as Daenerys? This idea necessitates that she be raised as Dany from the start to prevent her from having any memories of being called another name. Perhaps Lyanna just happened to name her that but this seems like an incredible coincidence. It also means that somehow Doran discovered the real Daenerys died and got the idea to ship Dany off to meet up with Viserys. Yet somehow Dany has no memories of first meeting Viserys as a little girl? She may have only been a few years old but surely she’d remember a time before Viserys who she assumes is her brother. Did none of her memories from back then involve him in any way?
Now let’s talk about her relationship with Viserys. If Dany is not Daenerys that would mean the real Dany died in some way. Surely Viserys knew. If we’re going to claim that a swap occurred without him knowing it brings up so many confusing issues. When did this happen? The easiest answer is that it must have been when Dany was fairly young since two babies with silver hair and purple eyes look close enough that he may not immediately notice. But that is obviously not the case. Dany’s memories involve her running through fields and looking out windows. She may have been a toddler, perhaps three or four, but she certainly wasn’t an infant. Children can look similar but not close enough for Viserys to mistake this strange girl for his little sister. He’s not a compte idiot. Also how did she get there before he noticed the real Dany was missing? Did he just not know about his sister’s whereabouts for over a month?
Ultimately Viserys had to have known but that’s not much better. If Viserys knew Dany is not his sister he would have asked for an explanation. What did Willem Darry or whoever gave him to Viserys say? Viserys never acts like Dany is not his sister but theoretically he could have just lied to her his whole life. Did he fear her having a better claim if she knew the truth? Why? She’s a woman and Aerys named Viserys his heir anyway. What lord in Westeros would back her over him? It can’t be because Doran already made a marriage pact between Quentyn and Dany because we know the pact doesn’t name them. Furthermore if Viserys is told “This is your niece Dany. She’s been living in Dorne but is now joining you” then he’d surely know Dorne is backing them even if he has no idea about the marriage pact with him and Arianne. Yet Viserys never gives any hint that he knows about his Dornish allies. He never reaches out to them for help. Perhaps he didn’t want to risk word getting out but his actions never seem to imply he knows a Lord Paramount is supporting him.
I could probably keep going but this is long enough. To date I don’t think I’ve seen a variation of the theory that addresses these potential issues but if someone can explain them I’d be interested in hearing their thoughts.
Tl;dr: Dany being anyone other than who she claims and/or growing up in Dorne creates a huge amount of questions and illogical character actions. As such I do not believe it but you’re welcome to try and CMV.