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Jeremy Liew got lucky. A colleague at Lightspeed Venture Partners told him that his daughter and her friends were hooked on a new app called Snapchat. Mr. Liew, sensing the next hot thing in tech, wanted to invest.

It took days for the venture capitalist to track down the young man behind the company, a Stanford University senior named Evan Spiegel, and then a dash of good fortune to persuade him to stop by Lightspeed’s office.

That meeting in early 2012 led to one of the most lucrative startup bets since the dot-com boom. Lightspeed’s $485,000 seed money, plus another $7.5 million investment, yielded stock that will likely be worth over $1 billion after the company now known as Snap Inc. prices its public offering expected Wednesday. Venture firm Benchmark, another early Snap investor, put in $24 million for a stake set to be worth about $2 billion.

Mr. Liew declined to comment about the IPO and the company’s future prospects.

Striking gold in the venture business is exceedingly rare, the product of not only investment acumen and business connections but also lots of luck. Blockbuster investments can cement a firm’s reputation for years to come, and give it an inside track on the next wave of promising entrepreneurs.

Accel Partners still basks in the halo of an investment made 12 years ago after its investment principal Kevin Efrusy got a tip from an intern at Stanford about a website called Thefacebook. Mr. Efrusy all but broke down the startup’s door to convince the company to take his firm’s money.

Accel’s $15 million investment ultimately returned $5.6 billion after Facebook Inc. went public in 2012, a nearly 400-to-1 payout, according to the firm’s spokesman.

Years of lackluster returns may have taken some shine off Kleiner Perkins Caufield & Byers, yet it still has a top venture brand name 18 years after it struck deals for dot-com era winners like Alphabet Inc., then called Google. That $12 million investment in 1999 reaped $4.8 billion for Kleiner, said a spokeswoman for the firm.

Kleiner missed the ensuing social-networking craze, betting on Friendster instead of Facebook, and steered vast sums of money into capital-intensive clean-technology projects, a troubled investment that is taking years for Kleiner to shake off. Kleiner did invest in Snap in 2014, and will roughly double its return in the IPO, and has had several successful investments such as in Nest Labs, bought by Google last year for over $3 billion.

Mr. Efrusy says finding startups like Facebook or Snap is akin to getting struck by lightning, but that smart investors prepare themselves by looking for companies and founders with unique characteristics. “You have to be holding a metal rod in a thunderstorm in the middle of Kansas,” he said.

Mr. Liew watches for social-media companies exploding in popularity among young women, who he says are the trendsetters.

Even for the best funds, the vast majority of venture deals aren’t lottery winners. Of the more than 14,300 U.S. companies that raised venture capital in the past decade, Snap will become one of just 30, or 0.2%, that later got valued in an IPO at $1 billion or more, according to Dow Jones VentureSource.

The venture industry hopes Snap’s offering ignites the IPO market, which dried up last year in part because public investors haven’t shown a willingness to pay up for private tech companies whose valuations rocketed past their business fundamentals. Fewer IPOs mean venture firms are struggling to turn their paper gains into cash.

Lightspeed, founded in 2000, hopes investments in Snap, and other companies like Nutanix Inc. and AppDynamics Inc. that have gone public or were acquired, will solidify its place as a top firm.

Back in 2012, Mr. Liew tried at least three different ways to reach Snapchat before he located Mr. Spiegel’s name. His lucky break was that Mr. Spiegel was a Stanford student, where Mr. Liew graduated, giving him access to the university’s Facebook group. Mr. Liew messaged Mr. Spiegel and got a response in minutes.

When Mr. Spiegel visited Lightspeed’s office he shared internal analytics data that showed user growth exploding. The 21-year-old impressed Lightspeed’s partners with his insight that evaporating conversations meant people shared more spontaneously on Snapchat than other social networks.

“Accidents don’t last,” Mr. Efrusy said. “Entrepreneurs get lucky, but they also have to be good. Look at the difference between the trajectories of Facebook and Myspace.”

Fears Snapchat was used for sexting were allayed by data that showed most photos were shared while teens were in school. About two weeks after that meeting, Lightspeed struck a deal while Mr. Spiegel was on spring break in Argentina.

Lightspeed’s trophy investment is slightly tarnished, though. A condition of the firm’s investment, earlier reported by the New York Times, guaranteed Lightspeed the right of first refusal to invest a large amount in Snap’s subsequent funding round.

The idea was to protect its economic interest in the company if things went well. But when a new investor, General Catalyst Partners, emerged in the summer of 2012, Lightspeed exercised its right to boost its ownership and that investor walked away. This angered Mr. Spiegel, who blamed Lightspeed for the broken deal, according to people familiar with the matter. Rival venture capitalists have seized on the episode, calling it a blemish on Lightspeed’s record.

A Snap spokeswoman declined to comment.

Mr. Liew declines to discuss the episode in detail. He still communicates on occasion with Snap executives, according to people familiar with the matter, contrary to rumors that all communication has ceased in recent years. He was in attendance at the company’s IPO roadshow event in San Francisco on Monday.