Lansman was brought up in an Orthodox Jewish family in Southgate, north London. He was a pupil at the independent Highgate School from 1970 to 1975. He first visited Israel when he was 16: "I worked on a kibbutz in the Negev and my aunt lived in Beersheba. It was actually a very politicising experience. When I did my bar mitzvah I saw myself as a Zionist and I think after I went there I felt it less. I was more interested in the kibbutz and what I liked about it was the pioneering spirit, the sense of community and radicalism of it."
He read for a degree in economics at Clare College, Cambridge, graduating in 1979. Later, he attended Birkbeck, University of London reading History and Politics graduating in 2007 with a Masters. He was active in the student union while at Cambridge University and was an elected student member of the Academic Board. Lansman ran for Union President with Andrew Marr on the same slate, then nicknamed 'Red Andy', who provided campaign cartoons. Soon afterwards he became a friend of Labour's election agent in Hornsey, Jeremy Corbyn.
During the Labour Party's early years of opposition following the defeat of James Callaghan's Labour government in 1979, Lansman worked as the "chief fixer" for Tony Benn. He was a prominent member of the Campaign for Labour Party Democracy (CLPD) and worked with Benn on his campaign during the 1981 Labour Party deputy leadership election. He was also the Secretary of the Rank and File Mobilising Committee (RFMC), which was the primary campaigning organisation for Benn. In 1981, Lansman "did surprisingly badly" but was successful in his election to the Labour Co-ordinating Committee.
During the campaign for the 1981 deputy leadership election, on the Weekend World discussion programme of 21 September, Denis Healey falsely accused Lansman of organising the severe heckling of speeches he had given in Cardiff and Birmingham. Lansman denied this was the case, as he had been in Spain during the Cardiff meeting and travelling to Aberystwyth during the Birmingham meeting. Healey later apologised for his mistake. According to Lansman, the producers of Weekend World, London Weekend Television, accepted he had been slandered and made an out of court settlement.
Mervyn Jones identified Lansman as part of a group on the left of the Labour Party that were "quite prepared to see a right-wing breakaway as the necessary cost of swinging the party in what they saw as the desired direction." Alongside Vladimir Derer and Victor Schonfield, Lansman was described as "unreservedly dedicated", with "no political ambitions of [his] own" and "in a position to work day and night for the cause without pay." Lansman later organised Benn's campaign in the 1988 Labour leadership election challenging incumbent Neil Kinnock, which Benn lost badly.
From 2010, Lansman worked as a researcher for Michael Meacher.
Lansman volunteered for Jeremy Corbyn's leadership campaign in the 2015 Labour Party leadership election, and was the sole director of Jeremy Corbyn Campaign 2015 (Supporters) Ltd, an official campaign company that held the data collected by the campaign. During the election, he was criticised for posting a link on Twitter to a Facebook page depicting rival candidate Liz Kendall as a future Conservative Party leader. Lansman's comments were condemned by a Corbyn campaign spokesperson, who said: "Jon Lansman's tweets are not on behalf of the campaign. We discourage all Jeremy Corbyn supporters from joining in with spoof websites or social media."
Following Corbyn's election on 12 September 2015, Lansman was a founder of the campaign group Momentum. Before the Labour Party Conference in late September 2015, Lansman was defeated by Michael Cashman and Gloria De Piero in an election for membership of the Conference Arrangements Committee, the body that sets the agenda for the Conference. Lansman is reported to be a supporter of mandatory reselection for Labour MPs.
In October 2015, he denied rumours that he was planning to stand to be the Labour Party candidate in Michael Meacher's constituency of Oldham West and Royton, which was due for a by-election following Meacher's death on 21 October.
Lansman was interviewed by The Jewish Chronicle in January 2016. He was asked about attitudes to Israel in the Labour Party and the attitudes of Jews towards it: "Yes, of course the vast majority of British Jews are supportive of Israel as a Jewish state – and actually so is Jeremy – but they are far from supportive of all aspects of what is currently happening there", he said. "I think Jews in Britain want peace too. I think Jeremy's message of fairness for the Palestinians is not something that will be rejected by the Jewish community."
At the end of April 2016, after long-standing Corbyn ally Ken Livingstone had made comments which led to his suspension from Labour Party membership, Lansman was quoted as saying: "A period of silence from Ken Livingstone is overdue, especially on antisemitism, racism and Zionism. It’s time he left politics altogether." A few days later, in early May, he wrote on the Left Futures blog that the use of the term Zionist to describe supporters of the government in Israel was "counter-productive". He cited one poll in which a larger majority of British Jews, 71%, favoured a Palestinian state, and 75% opposed the Israeli settlements, while only 68% identified as Zionists. A "rational debate about how to change the terms of the current debate" requires, in Lansman's opinion, an acknowledgement "that people on the left may also demonstrate some prejudice of their own."
"I think progress has been uneven; let’s put it that way", he told Daniella Peled, a London-based reporter for Haaretz, in September 2016. Developments in Labour concerning antisemitism since the beginning of the year have "clearly taken us back as well as forward". Lansman cited the Chakrabarti Inquiry as an example of the latter.
Lansman's wife, Beth Wagstaff, died of breast cancer in January 1999 aged 39; the couple had three children. Lansman has been a trustee of the charity, Breast Cancer Care, under whose auspices his wife had set up the Lavender Trust before she died, both to help younger women become aware of the disease and to support them.
Lansman is an atheist, although he still observes some Jewish festivals.