LYNN – They were generally pleased with the city’s response to nature’s one-two snow punch Sunday, but locals shoveling out cars and driveways Monday said the city should do more to ensure all drivers abide with street parking bans.A car parked in front of Dwayne Horton’s driveway forced plows to swerve around the vehicle and deposit an ever-expanding snow mound in front of his car. He spent Monday morning shoveling out along with neighbors like Derek Murray.”The city could have towed more. It just makes it tougher to clean the streets,” Murray said.The city imposed a street parking ban from 1 p.m. to 9 p.m. Sunday to allow plows to clear streets. Public Works Commissioner Jay Fink said the ban was lifted based on late evening/overnight predictions of one to two inches of snow. Fink explained why he did not alter the ban.”We didn’t because we thought it was grossly unfair to have someone go to bed thinking it was one to two inches and then getting six inches and having hundreds of cars towed. Two plowing events in a 12-hour period is unheard of,” he said.Fink said he coordinates with police and city parking officials to ensure vehicles are towed off streets before the plows roll but he said drivers need to do their part to move vehicles, especially off main roads.”It’s problematic on main streets: If we can’t get snow cleared before it freezes we never will,” he said.He gave city plowers and contractors high marks for clearing main streets and side streets following a storm that dumped light snow early Sunday morning. That initial snowfall was followed by several inches Sunday night into Monday morning.City snow ban rules require drivers to remove vehicles from streets or risk ticketing and towing to the Bennett Street yard near the River Works.The city announces the ban online and on cable television and alerts drivers by lighting blue intersection lights across the city. School yards and major parking lots including the Market Street commuter garage are available for overnight parking. Drivers who park in school yards must move their cars by 6 a.m. the next day.Zobaida Santo parked three blocks from her house to get her car off the street and cleared it off Monday before starting to clear her mother’s vehicle. With winter barely a month old and already dumping several storms on Massachusetts, Pete Corbett would like to see the city crack down on home and building owners who do not shovel sidewalks in conformity with city ordinances.”Landlords should be fined,” he said as he shoveled his walk.Fink urged people shoveling and snow blowing to keep snow off streets and clear sidewalks.