Lipman, who is a rabbi, was hit by the stone shortly after immigrating to Israel from the United States, eight years ago, when he stumbled into a riot over plans to dig up some ancient bones - something the protesters said was a desecration.
"We have returned to this land after 2,000 years and we have to get this right; and it is not right," said Lipman, a member of the Yesh Atid party that wants Israel's large ultra-Orthodox communities pushed into mainstream society.
An integral part of Prime Minister Benjamin Netanyahu's ruling coalition, Yesh Atid is leading an unprecedented, multi-pronged charge, backed by legislation that seeks to draw more ultra-Orthodox men into the conscript army, trim their welfare benefits and reform their antiquated, religious schooling.
For many haredim - a Hebrew term meaning "those who tremble before God" - the government is doing too much too quickly. Even some coalition partners have their doubts, fearing a backlash from the volatile fringe of a disparate movement born in the impoverished villages of 18th-century eastern Europe.
The haredim make up 10% of Israel's eight million population and they are expanding rapidly, with families of 10 children not uncommon. Few of them share Lipman's world vision.
Often living in de-facto ghettos of their own making, the majority of haredi men are allowed to shun the army and dedicate their life to religious study, living off donations, state benefits and the often meager wages of wives, many of whom work.
In a country where most 18-year-old Jewish men and women are conscripted, to maintain a standing and reserve army over 600,000 strong, such treatment is causing growing resentment - something Yesh Atid successfully tapped into at an election in January, helping it become the second largest party in Israel.
As a result, haredi parties were cast into opposition for only the second time since 1977, leaving angry ultra-Orthodox to warn that the rule of law cannot trump the rabbis' word.
"We'll go to jail. Don't put us to the test," said Yechezkel, a 30-year-old, full-time seminary student, wearing the traditional heavy black garb that many haredi men don, in defiance of the sun burning the Jerusalem street around him.
Ultra-Orthodox men poured onto the streets of Jerusalem last month to protest against government plans, hurling stones at police at the start of what could become a long, hot summer.
"It's a joke. They founded a state 65 years ago and they want to reform people who keep a thousands-year-old tradition," said Yechezkel, contrasting the devout to the secular Zionists who founded the Jewish state but kept religion at arm's length.
He declined to give his family name. As he spoke, a passerby shouted that it was blasphemy to even talk to reporters at all.
Studying the Jewish scriptures, the Torah and Talmud, is one of the most important edicts for the haredim, whose heroes and role models are rabbis and scholars who stood against religious changes that reached Jewish communities with the industrial age.
However, ultra-Orthodox moderates such as Lipman deny that study should exclude all else, pointing to the United States where haredim have full-time jobs - including his father who was a judge and whose old gavel sits on his desk besides the stone.
In a country that feels under siege, with a 20% Arab minority and Jews themselves drawn from very diverse immigrant groups, the separateness of the haredim has come to seem a major obstacle to Israel's national cohesion as their numbers swell.
When the state was created in 1948, its first prime minister, the Polish-born socialist David Ben-Gurion, exempted about 400 students from military service so they could devote themselves to religious study, hoping to keep alive sacred knowledge and traditions almost wiped out in the Holocaust.
Fast forward 65 years, and the number of full-time seminary students has swelled to about 60,000, across a wide age range.
Demographics suggest their ranks will expand much faster in the decades to come, with an estimated 32% of all Jewish children who started school in Israel last year going to haredi establishments – most of which barely teach subjects such as math, concentrating instead on the Jewish scriptures.
"The fact they don't serve and they don't work is starting to be a real problem for the economy and for the unity of Israel," said Ofer Shelach, another Yesh Atid lawmaker, whose secular background is more typical of the party's electorate.
"If we don't prepare them better, our workforce will be ruined," he told Reuters, arguing that getting more haredim to serve in the army was a good way to teach them new skills that would eventually help them find jobs.
Such arguments hold little sway in the haredi Jerusalem neighborhood of Geula, where the narrow streets are crowded with men, women and children who appear to have stepped out of grainy photographs from pre-war eastern Europe.
"It seems we live on different planets," said Mordechai Wingott, who lectures in a seminary for teachers. "These are different cultures, with different values. Lack of understanding creates hate and divide. Suppression is done for its own sake, not for the sake of the budget or equality," he said.
Under the terms of the conscription bill that is due to be passed into law by August, only 1,800 seminary students will be allowed to skip military service each year out of 8,000 ultra-Orthodox religious students reaching service age each year.
Through a mix of incentives and threats, including possible jail terms, the government hopes the remaining number will gradually be drawn into the military, or alternative civilian service roles. Haredi women will retain their exemption.
But street posters have already gone up in Geula, calling on young haredi men to go to prison rather than join the army, voicing the fear that the sheltered youths will be corrupted by the modern world if they leave the yeshiva seminary schools.
"The new Israeli government is definitely more hostile to the ultra-Orthodox people, our way of life. They are trying to destroy it," said Michal Green, 48, a mother of seven who compared it to historic enemies of the Jews. "The Jewish people are used to (others) trying to destroy them," she added.
Not all haredim are against military service. The military says some 3,500 soldiers serve in units or in army roles where conditions are designed to cater to their strict religious codes, and the numbers are slowly rising.
Life is not easy for them. David, a 24-year-old network manager in the army, said many haredi soldiers were afraid of being shunned by their families for serving in the ranks. He did not give his full name because he did not want to be identified.
"I come from a more moderate family," he said. "I can come home in uniform but some of my friends can't. They keep secret the fact that they are in the army. As soon as they leave the base for home, they change into civilian clothing."
Underscoring the pressures they face, one poster in Geula described haredi soldiers as sinners who shunned their forebears by joining the army of the Midianites – a Biblical people who hounded the Israelites, according to the Old Testament.
David said he decided to enlist in order to increase his chances of finding work: "You get experience in the military and the army also gives you professional courses," he said.
A recent study by the Economy Ministry found that 70% of haredi soldiers entered the workforce after they completed their service. By contrast, only 45% of all haredi men were employed, according to the Israeli central bank.
The government believes many ultra-Orthodox are tired of relentless poverty and, unable to challenge the authority of the powerful rabbi, secretly hope the reforms triumph.
In a further effort to encourage the haredim to seek jobs, the government is going to cut child welfare for large families and says it will withhold funds from schools that do not broaden their curriculum and prepare their students for the workplace.
David Zoldan, a journalist and one of the first haredim to serve in the army, says his community is in fact ready for change, but warns that threats and edicts are not the way forward: "Once the haredi public decides it is not going to do something, it will not budge," the 32-year-old said.
"It must be done with consent, otherwise it is doomed."
His concern is echoed by some government allies, who fear the proposed pace of change will prove counterproductive.
"I am against any reform that is taken very dramatically and very sharply in just a short period of time," said Silvan Shalom, Israel's energy minister and a political heavyweight in Netanyahu's traditionally secular, right-wing Likud party.
"We have been a nation for just 65 years. We were in exile for 2,000 years. After so many years, you are going to have tribes," Shalom told Reuters. "It seems like Israel will remain a country of tribes for many decades."
Such sentiment raises the question of how vigorously the draft bill will be enforced. According to the current version, it will only come into full effect in four years, when a new government that could include haredi parties, will be in office.
"It's a massive scam," said Shahar Ilan, vice president of Hiddush, which campaigns to limit the legal power of certain religious leaders over the life of Israel's Jewish citizens.
"They are leaving the fight for the next government."