To know if the guy is potentially lying, what you do is look at what the character does. Mr. House is shown to be ruthless and a little eccentric, but never once is he shown to be a liar. In fact, if the character has any flaws is the fact that he's too honest. He sees human interaction as a purely logical game of exchanging value. He always trust people to be logical and act in their best interests and doesn't realize sometimes people are just too stupid to understand what their best interest are, like the Omertas, who despite having money and power and living in luxury want to side with Caesar, under the impression that they will rule Vegas, even though anybody who has even superficial understanding of what the legion is could tell you why they're essentially committing seppuku.
Now, is he actually capable of achieving what he promises? Well, why wouldn't he? He's responsible for most of the advanced technology you find in game. He saved himself and Vegas from the total nuclear destruction that consumed the entire world. He has the means and the knowledge to achieve what he wants. I've seen people who are so irrationally skeptic of the idea but they've never been able to produce a good reason why. One guy in fandom (BTW don't ever go to fandom, I made the mistake and it's a total cesspool) told me "space travel for a post apocalyptic society is just pie in the sky". That was his whole reason. As if 100 years of economic and industrial development, combined with all the amazing pre war scientific knowledge wouldn't be able to produce space travel in any society.
Ultimately it's never an issue for me because here's the thing. In a world that has been turned into a toxic ruin, there's nothing more important than abandoning Earth. Maybe House can't deliver on his promises. But if House can't, the courier can't, and NCR sure as hell can't, and the Legion, well, it doesn't even need to be said.