Drivers who do not pass the yearly background check and continuous screenings will be prohibited from driving on the platform.
Lyft's stock began trading on the Nasdaq on March 29 under the ticker "LYFT."
The strike resulted from an Uber policy that slashed pay-per-mile by 25%, bringing the rate from 80 cents per mile to 60 cents per mile.
The zones will first be designated in the Fenway neighborhood, near the dining and night life hubs.
The ride-hailing company also reported a loss of $911 million.
Metro's board of directors is hoping that adding on a tax will discourage "single passenger" rides, and promote carpooling and public transit.
Lyft plans to go public before rival Uber.
The ride-hailing company says weakening the standards will hurt its business, as it needs automakers to produce fuel efficient vehicles en masse.
For the 2020-2021 budget, $2.58 million of the total $5.6 million has been derived from ride-hailing groups.
Customers also ranked Lyft as their preferred rideshare service.