Writing in The Times, the former chancellor said there was now a "clear" case for withdrawal, insisting the economic benefits would "substantially outweigh the costs", in contrast to the Prime Minister's position.
In a move that piles further pressure on David Cameron over the issue, he warned the prime minister's proposed renegotiation would only secure "inconsequential" concessions from Brussels.
But Downing Street said the prime minister remained "confident" that his strategy "will deliver results".
Mr Cameron is already under pressure to hold a "mandate referendum" as early as next spring to seek public approval of his strategy of putting a renegotiated settlement to an in/out vote by 2017.
In the wake of Ukip's surge in last week's county council elections, there is also pressure to put the strategy to a vote in the Commons in defiance of his Liberal Democrat coalition partners.
On Tuesday morning Ukip leader Nigel Farage said Lord Lawsons article in The Times "legitimises the Ukip position and exposes serious divisions in the Tory Party".
Lord Lawson, who was Margaret Thatcher's longest-serving chancellor and remains a highly-respected figure within the party, said that it was "by no means assured" that Mr Cameron would win the 2015 general election.
But he said he believed public demand was such that a referendum would have to happen under Labour in any case.
Dismissing the chances of either party securing significant reforms, he said Brussels would fear a "general unravelling" as other countries sought to match the return of powers.
"But all this is largely beside the point," he wrote. "The heart of the matter is that the very nature of the European Union, and of this country's relationship with it, has fundamentally changed after the coming into being of the European monetary union and the creation of the eurozone, of which - quite rightly - we are not a part.
"That is why, while I voted 'in' in 1975, I shall be voting 'out' in 2017.
"Not only do our interests increasingly differ from those of the eurozone members but, while never 'at the heart of Europe' (as our political leaders have from time to time foolishly claimed), we are now becoming increasingly marginalised as we are doomed to being consistently outvoted by the eurozone bloc.
"So the case for exit is clear."
While there would be "some economic cost" from leaving the EU single market, he went on, "in my judgment the economic gains would substantially outweigh the costs."
That would not only be in keeping the UK's £8 billion net contribution, but also being removed from excessive bureaucracy, not least the "frenzy of regulatory activism" affecting the banking sector.
"The foolish and damaging financial transactions tax, imposed against strong UK opposition, is only one example. In part this is motivated by a jealous desire to cut London down to size, in part by well-intentioned ignorance," he said.
"The Bank of England is becoming increasingly frustrated by the mandatory nonsense emanating from Brussels.
"Escaping from this and reinforcing the escape by co-operation with the only other genuine world financial centre, the United States, would be a major economic plus.
"Those who claim that to leave the EU would damage the City are the very same as those who in the past confidently predicted, with a classic failure of understanding, that the City would be gravely damaged if the UK failed to adopt the Euro as its currency."
Quitting the single market would only have "marginal" disadvantages, he suggested, and could even have "a positive economic advantage to the UK" by forcing British firms to look further afield.
Too much UK business and industry felt "secure in the warm embrace of the European single market and is failing to recognise that today's great export opportunities lie in the developing world", the peer wrote.
"Just as entry into the Common Market half a century ago provided a much needed change of focus, so might leaving the EU, an institution that has achieved its historic purpose and is now past its sell-by date, provide a much-needed change of focus today."
Liberal Democrat leader Nick Clegg said leaving the European Union would jeopardise jobs and make Britain less safe. "I think if we were to leave the European Union we would jeopardise up to three million jobs in this country," he told ITV's Daybreak.
He added: "We would make ourselves less safe - we work in the European Union to go after criminals who cross borders, it would be more difficult to deal with environmental challenges which cross borders.
"We would not be taken as seriously by the Americans, for instance, who like the fact that we stand tall in our own European back yard .
"I know the Conservatives are struggling to work out how to deal with Ukip and they keep now changing their minds - one moment they want to be in the European Union, now senior Conservatives like Nigel Lawson say they want to go out.
"I think we need to reform the European Union to make it more transparent, more efficient, more democratic where we can but not turn our backs on it because doing so would make us less safe and less prosperous."
A Downing Street spokesman said: "The PM has always been clear: we need a Europe that is more open, more competitive, and more flexible; a Europe that wakes up to the modern world of competition. In short, Europe has to reform.
"But our continued membership must have the consent of the British people, which is why the PM has set out a clear timetable on this issue."