I am of two minds on his knowledge gap. On the one hand, you’d think that the man whose several companies, including the much-criticized deal-promotion site Groupon (GRPN), occupy what once was Ward’s headquarters, would have the curiosity to know about its demise in 2001. (After limping along for decades, the sick man of discount retailing liquidated its remaining 250 stores and fired 37,000 employees.) On the other hand, Lefkofsky arrived in Chicago in 2004 and isn’t a backward-looking guy. Technology entrepreneurs often are at their best dreaming up the future, not dwelling on the past.

The question, then, is whether Groupon is a footnote to the Internet era, a four-year-old pup of a site worth $4 billion that has suffered more than its fair share of ups and downs, or if, as Lefkosky believes, it enjoys a brilliant future built on its impressive collection of customers and merchant/partners.

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I’m meeting with Lefkofsky on a brisk spring day in Chicago at the unreasonably early hour of 7 a.m. The football-filed length of cubicles of Groupon’s headquarters are nearly empty when we sit down in his spartan office. The single notable furnishing is a 10-foot-wide printed-out organizational chart of Groupon’s complex corporate structure. We meet a couple of months after Groupon fired its founding CEO, Andrew Mason, naming Lefkofsky, another founder, the co-CEO along with fellow board member Ted Leonsis. (Leonsis, a former top executive at AOL (AOL) knows something about beaten-down consumer Internet companies.) It also is the week before Groupon releases first-quarter earnings, a report on Wednesday that saw revenues increase 8% year over year to $601 million and operating earnings of $21 million, a decrease from the year earlier but an increase from the fourth quarter.

The purpose of our meeting seems to be to convince me of Groupon’s staying power, and so I need to confess something right away: I can’t help but like Groupon. Unlike some writers who cover the company, I won’t fake having bought some “groupons” to experience the product. I did once or twice when it was new. But it’s not my thing. I’m not the right demo. (Groupon’s “power user,” in fact, is a 42-year-old, urban mom with two kids, household income of $100,000, and an iPhone.) But I do admire this plucky company’s ambition, its unwillingness to accept defeat just because it failed to sell out to Google (GOOG) when it had the opportunity, suffered under an inexperienced CEO, and repeatedly disappointed Wall Street. There’s a never-say-die attitude about Groupon, and it is admirable — whether or not it ultimately succeeds.

Lefkofsky says Groupon’s goal is to simplify the company, but adding complexity by diversifying away from daily deals is its best chance for success. He says the company is trying not to spam its users with so many emails, currently about two a day. Revenue from responses to emails is around 45% of the total now, down from 90% a year ago. In its place is a greater reliance on events and goods offered for sale until they sell.

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The big change is mobile. Groupon says 45% of its sales come from its mobile apps. “By virtue of the Groupon business model, we just happen to be perfectly situated for mobile,” says Lefkofsky, adding that “no e-commerce company is close” in terms of mobile as a percentage of its sales. He’s talking about e-commerce giants Amazon (AMZN) and eBay (EBAY), both heavily reliant on Web activity.

Groupon also is trying to get away from what was a novelty, getting a great deal on something you didn’t know you wanted, to offering deals on things customers are looking for. It also is pushing merchants to sign contracts to offer products perpetually, as opposed to one at a time. He says merchants, despite the publicity of those who say Groupon customers are only looking for a deal, value Groupon for new customer acquisition. “We surveyed two million customers,” says Lefkosky. Eighty percent said they were either new customers or hadn’t been back to a merchant recently.

You’d think from all that’s gone wrong at Groupon — its European operations are a mess, it fired Mason, its stock cratered — that the company would be retrenching. Employment in fact is down, but the young company still has 11,000 employees. It has engineering centers in Palo Alto; Berlin; Santiago, Chile, and other places.

What’s more, Groupon thinks it has a whole new approach to retail pricing. Jeff Holden, an Amazon veteran who heads product development for Groupon, suggests that Groupon can use its giant merchant and customer rolls to introduce dynamic pricing that mimics the success of airlines. It’s “completely ridiculous,” says Holden, that a restaurant would charge the same for a meal on an evening when the joint is empty than when it is jammed. Airlines figured this out a long time ago, and restaurants, using Groupon’s ability to target local customers, adjust their pricing opportunistically. “There’ll be a street price and a Groupon price,” says Holden.

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This all makes good sense, and it occurs to me given the lack of overlap with eBay and Amazon, Groupon would be a nice tuck-in acquisition with one of those giants. Lefkofsky is adamant that Groupon, having passed on the ability to sell once, isn’t any more interested now.

By the time I’m getting ready to leave, Groupon’s offices are buzzing with employees, many of whom are working the phones to convince merchants to offer deals on Groupon. I ask Lefkofsky if Groupon will miss Mason’s whimsy, one of his endearing qualities that gave the company some its edge. He refers me to his letter to shareholders in Groupon’s annual report that lists the company’s five core values: “Start with the customer and work backwards. Great people make great companies. Be intolerant of mediocrity. Build for the long-term. And make life less boring.” Life at Groupon has never been boring — and isn’t likely to be any time soon.