There's no explicit proof to the player... The dad was there, he would have seen her burial or cremation. He's not gonna forget or confuse something like that... But yes, we don't see that scene.
There's literally no evidence or even the slightest indication that the dad is a liar. He's a very genuine, good dad who raised his son to have good morals.
Is there a possibility that the dad is hiding the truth? Sure. Is there the possibility that the dad is actually an alien and has been grooming the mc to save the universe? Sure. Are any of these indicated so far in the game? Absolutely not.
So yes, any random theory that has no basis from within the game can be stated, but just because it can't be refuted with proof, doesn't make it a good theory...
So:
- The dad lying about the MC's mom's death is not based on any evidence in the game whatsoever. It's not a good theory.
- The dad being an alien and grooming the mc to save the universe is not based on any evidence in the game whatsoever. It's not a good theory.
The dad isn't an unreliable narrator. He's not even a narrator.
The mc's quote regarding the dad's (un)reliability is as follows:
"My mother died shortly after giving birth to me."
"It's a shame that I never got to meet her."
"I would have loved hearing stories from her past and truly getting to know her."
"Sure, my dad told me stories growing up...but his memory sucked."
"He would always forget the punchline. Not surprising, since he would talk so long before reaching the point where the punchline was supposed to be."
The only example we get of this is as follows:
Neil: "But your mom, stubborn as a mule, didn't give up that easily."
Neil: "It took her three days to run away from home and track me down."
Neil: "No...wait...five days?"
Neil: "Hm...maybe it was something along the lines of a week?"
mc: "Are you seriously asking me that?"
Neil: "No, well, it was something like that."
Neil: "Either way...where was I?"
Neil: "Oh yeah!"
Neil: "She didn't want her dad's life or his money..."
So he rambles a bit, loses the point a bit, and inconsequential details like how many weeks between him leaving and Lynette coming to find him are not crystal clear. In no way does that make the core of his stories unreliable, or does it set him up to be a liar. What, he just forgot that Lynette didn't die?
When the mc says the dad's memory sucked, he then followed it up with an example ("forget the punchline", "talk so long before reaching the point"). It doesn't give the impression his dad has Alzheimers...
Neil: "Your mom was a very beautiful woman. I was 24 and she had just turned 18."