"Lean" in this context doesn't mean "cheap." http://steveblank.com/2009/11/02/lean-startups-aren%E2%80%99...
The key point from the article: "If you confuse Lean with Cheap when you do find a repeatable and scalable sales model, you will starve your company for resources needed to scale."
Your point about lean and cheap is fair but a bit confusing in context.
The reason this works is because once you have that repeatable and scalable business model, you can be fairly sure that hiring a person (plus all the other operational costs) at $X will bring in >$X in new business. So you spend money for growth; the expenses are booked this year, the revenue doesn't happen until next year when contracts are inked, product improvements are launched, more people hear about Square, etc. The number to pay attention to is gross margins (the amount of money they make off each transaction); the 2nd article I linked lists that at 34%, which is comparable to Amazon's 30% and Apple's 39%. As long as that is positive and high enough to cover fixed operational costs, Square can instantly get to profitability by laying off people (or, with current revenue growth, simply by slowing down hiring).
The risk with this strategy is that the market turns out to be smaller than expected, and your product appeals only to a small number of early adopters. Growth then slows down markedly right as expenses ramp up, and there's no way to jump-start growth again. I think this is what's happened with Quora. Square seems different, though: the customers I've talked to are decidedly non-technical, and yet they love the product.
I know an engineer who works at Square, they are not a lean startup, they have all the various excesses that people love to hate which is expensive catering, free shit, expensive furnishings. Square is not lean, and when you're losing $100,000,000 a year, I don't care if you're an ancient business like Ford or IBM, that's not good, and you wont have 7 years to reach profitability profitability, you got about half that, if you don't hire anymore. If Square stops hiring, that's also not good. They're going to have to let people go, like their recruiting operation, which is world class.