Uber faces a deadline to go public by September 30, and a filing this week suggests the debut will come earlier than that. A year ago the company's cofounder and former CEO Travis Kalanick resigned from his position following a tumultuous six months of scandal.
Uber, which now has a market valuaton of $76 Bn (INR 5.42 Lakh Cr), has been one of Silicon Valley's most controversial companies.
Lyft's last valuation was at US$15 billion during a private fundraising round.
The company filed confidentially for an IPO on Friday, marking the beginning of a race for the two ride-hailing giants to the stock markets.
Uber exited other countries because it had a smaller market share and was burning a lot of cash.
Both are expected to be among next year's largest offerings.
For now, Uber has further increased its losses in the third quarter to more than a billion dollars.
An IPO of such magnitude would especially be a mark of investor confidence for Khosrowshahi, who replaced the controversial Travis Kalanick, pushed out the door by investors anxious over a string of scandals.
The filing by Lyft, which hired JPMorgan Chase & Co, Credit Suisse and Jefferies as underwriters, plants a flag in the ground to go public before larger rival Uber. Uber's food delivery service UberEats has also grown seven times over the past four months.
The ride service was set up in 2012 by entrepreneurs John Zimmer and Logan Green and has raised close to $5 billion from investors.
"With autonomous cars on the horizon, it is anyone's guess where this sector goes in the future", said Jeff Zell, senior research analyst and a partner at IPO Boutique in Florida.
Lyft presents other risks, including unresolved questions about its workforce of independent contractor drivers.
Nonetheless, today Uber is in a much better position than it was a year before.