It's highly unlikely <PERSON> painted these and lied about it:
* <PERSON> would somehow have had to brush up on ancient and mystical knowledge on the Children of the Forest's symbology in order to make these seemingly accurate drawings.
These symbols you see bear significance in the culture of the Children of the Forest, which in turn is reflected in the White Walkers (which are created by the Children of the Forest)
The spiral cave painting here on the left coincides with the same geometric pattern that the White Walkers put together using corpses in Season 3.
Another spiral pattern, here seen in a top-down view of one of an elaborate monument made by <PERSON>, where we have Stonehenge-style standing stones in a spiral pattern, seen in S06E05. The creators of the show talk about this pattern in this scene on 'Game of Thrones Season 6: Inside the Episode #5'
Here we have what looks like the Greek symbol, phi ('Φ'), on the left coinciding with the same geometric pattern of corpses that the three rangers in S01E01 run into, also put together by <PERSON>.
The only Westerosi people who might know this much about the White Walkers, Children of the Forest and their symbology are <PERSON>, <PERSON> (Three-eyed Raven) and perhaps some members of the <PERSON> family. Neither <PERSON> nor <PERSON> would know these things. While the Night's Watch and the Wildlings are aware of these symbols made by the White Walkers, they wouldn't make the connection with the Children of the Forest, so for <PERSON> to paint these symbols and attribute them so confidently to the Children, while being very accurate, seems extremely far-fetched.
This whole idea of <PERSON> faking the cave paintings is essentially debunked, implicitly, by the creators of the show in 'Game of Thrones: Season 7 Episode 4: Inside the Episode (HBO)', where D&D discuss the importance of the symbols in the cave and how it relates to <PERSON> and <PERSON>.
- <PERSON> would have to have had blue paint on-hand
Close-up of the cave painting of <PERSON> and his White Walker lackeys. 520
The blue in their eyes stands out as quite intense and vivid.
Blue is historically the most difficult colour to make pigments and dyes and paints of, in our world.
If we assume the fan-theory to be true, then we also have to assume <PERSON> brought blue paint with him to Dragonstone, just in case he needed to draw some White Walkers in a cave, just in case <PERSON> didn't believe him. It's not impossible, but not very believable.
Incidentally, on the topic of blue, I found this quote on Wikipedia:
Reds, blacks, browns, and ochres are found in cave paintings from the Upper Paleolithic period, but not blue.
—Blue (In the ancient world), Wikipedia
It's an interesting, funny fact that would coincidentally lend credence to the fan-theory, but one shouldn't compare non-fictional, early Homo Sapiens from the Upper Paleolithic era with fantastical, magical, spell-casting Children of the Forest in a fictional setting, in order to arrive at conclusions about the availability of pigments for cave paintings.
* <PERSON> would have to be a skilled liar
<PERSON> is honourable and true (not a trickster or liar), much like his surrogate father, <PERSON>.
The last time <PERSON> specifically lied was when he had to deceive the wildlings into believing he was a turncoat crow - he even killed <PERSON> to sell this deception.
The thing is, he was already sexually attracted to <PERSON> and was starting to have conflicting feelings about the wildlings, and the pointless violence between them and the Night's Watch, and he was starting to see that what he was told about the wildlings wasn't true, after spending some days with <PERSON>. Had he not had these conflicting feelings, he would have executed her when he had the chance. All this to say: he didn't really lie, so much as he was following <PERSON>'s orders, and leaning into his true, new, growing feelings about the wildlings.
It would be very unlike <PERSON> to lie to <PERSON> about this, not to mention the risk of getting caught lying, whether because he was spotted by guards carrying paint around, or spotted in the middle of painting, etc. would jeopardize the entire mission (the most important mission in the world) of getting help for the War for the Dawn - a very high risk. 247