The strike, planned ahead of Uber's Friday initial public offering, is being backed by the New York Taxi Workers Alliance.
Lyft's stock began trading on the Nasdaq on March 29 under the ticker "LYFT."
The ride-hailing company also reported a loss of $911 million.
Lyft plans to go public before rival Uber.
Although Lyft trails Uber in terms of value and market reach, experts said beating Uber to IPO will give Lyft an advantage, as the added attention will cement Lyft as a viable alternative to Uber.
If the San Francisco-based ride-hailing app goes public with that value, it would be worth three times as much as Ford, and more than twice as much as Tesla.
According to sources, who declined to be named because the talks are private, the companies have discussed numerous potential deal structures, but haven’t come to a final agreement.
HyreCar has granted the underwriters a 45-day option to purchase up to 378,000 additional shares of common stock at the IPO price less underwriting discounts.
HyreCar has reportedly already raised $5.5 million in venture capital funding.
The Brazil-based car rental company has filed for an initial public offering and hired several banks to underwrite the transaction.