I'm going to offer an alternative, completely opinionated answer to this question. Like @Napoleon Wilson I'll focus on the life lessons you brought up. However, I'm not going to focus solely on House, but also the context in which he said them and the show revealed them.
Brace yourself - a long and completely subjective post is ahead.
At first glance, this seems a simplistic statement to understand. Everybody lies about something. I would agree with this. Whether the lies be great or small, everyone tells them.
But the show never implies the lies are small. This line is frequently used to describe some huge secret that characters on the show have. In fact, I found this to be one of the disappointing things about the world of House. It's almost guaranteed that if a man comes into the hospital with his wife and refuses to leave her bedside because he cares so much, it's really because he is responsible for her illness, or he cheated on her, or he embezzled money, or something other than genuine sorrow and support.
This is one of the life lessons from the show that I think is unfair and not true. As I said, I understand the basic sentiment is correct, but the show uses it to imply that everyone has a life changing secret which affects the treatment options available, which I think is categorically untrue.
Whilst it was fun to watch House, and whilst this statement is in general true, given the context in which this statement was used on the show, I disagree with it and don't think it can be called a life lesson.
Everyone is an idiot.
@Napoleon Wilson made excellent points about this statement, discussing how everyone appears inferior to House and their emotional sacrifices offer themselves up to his scorn.
But it's also worth pointing out that the majority of House's treatments are extremely unusual and dangerous. Is it idiotic for patients to opt against treatment suggesting by him, when other doctors strongly advise against it?
Not to mention how often in the series House and his team require multiple diagnoses before reaching the correct solution (think how many episodes begin with multiple wrong treatments before the correct one).
Obviously no doctor can be right every time and given the unusual nature of his team's cases, it's only logical that multiple approaches are required to successfully diagnose patients - but often all of these treatments are highly dangerous and thus it seems unfair to label all patients on the show as an idiot if they don't immediately follow his advice.
So, to him they may well appear that way, but it seems wrong to consider this a life lesson.
In fact, if one references Gardner's Theory of Multiple Intelligences it can be seen that in general people have intelligence in a range of areas. Again, it seems harsh to label everyone as idiots simply because they don't have intelligence in the medical sector.
Parents mess up their kids, regardless of being a good or bad parent.
This is very subjective and extremely difficult to accurately judge. Define mess up their kids? Does it mean they give them life long phobias over things (such as my own father telling me to never ride a motorcycle and that lifelong lesson still holding today, for no logical reason?). Does it imply that every child has severe trauma due to their parenting?
I would argue that a simple look around the world should show that there are plenty of perfectly healthy, rational, happy adults who love their parents and had a happy upbringing.
That's not to say they haven't had life lessons imparted on them or had sanctions placed against them - but rather that they are not simply messed up.
Relationships usually don't work.
Again, it's hard to know where to draw the line with this. Does it refer to only serious relationships? If so, what is serious? Does it refer to marriages? Simple searches online show that slightly more than 50% of marriages are happy and last for life, suggesting relationships of that caliber usually (but not always) do work.
But if this statement refers to all relationships, then it seems very likely it's true. After all, not many fifteen year olds who date for two weeks expect their relationship to last.
People have to lie to make people happy.
This seems unlikely for reasons similar to the first question. I'm not implying people never lie, but it appears unfair to label everyone as requiring to lie for the sake of happiness. I've told lies in my own life, but I've never felt the need to lie to someone's face to make them happy.
But even if I did, where do you draw the line? If you tell someone they look good, despite the fact you don't think they do, does that meet the criteria? Does it matter who you say it to? If I meet someone and tell them it's nice to meet them, despite my feelings to the contrary, does that count?
If so, then again, like the previous statement, it appears logical that this could be true. But given the context the show implies it in, that serious lies are required frequently for anyone to be happy, I disagree with it.
Gregory House is mentally insane?
I would definitely disagree with this. Medical insanity is about an unsoundness of mind and an inability to rationally act in a way a reasonable person would. Whilst House may appear to frequently act in a manner not consistent with a reasonable person, he is most certainly of sound mind as any observation of him and his work uncovers.
The best patients are the ones who can't respond.
There are some cases even on House which shows this isn't the case (such as where if a patient could utter a single word about what happened to them, or where they got ill, the case could be solved immediately.
Probably a better phrase would be "the quietest patients are the ones who can't respond"!
Okay, okay, I know I took this way too seriously, but I wanted to simply comment that in the context of the show, whilst these lines are frequently shown to be true, in real life it seems unfair to assume they would be.
Remember, House is the ultimate, bitter, lonely cynic and these comments all shape his own views of the world. As we see the show through his eyes and we see mostly his successes, it appears like his life lessons hold true. But it's just a show - a show in which everything is designing to enhance his intelligence.
How often do we watch a show or movie where our hero goes on a vendetta against the bad guy? Often with no evidence or proof, but he's vindicated in the end as some scrap of evidence shows up and he gets his bad guy... Except what if he didn't get him? What if he was actually innocent and all we've watched is harassment? This would completely betray all the motives and beliefs and ideas of the supposed hero and make a mockery out of his goals - except we rarely see that side of events occurring.
What I'm effectively saying is, House's lessons look brilliant and true because the show frequently shows them that way. In real life, is it likely that almost every couple who end up in hospital are lying to each other over serious issues? Perhaps. But, like many of the other life lessons, I just don't believe it.