Lew's comments echoed those of chief economic adviser at Allianz, Mohamed El-Erian, who told CNBC on Tuesday that there was an increasing probability of a financial "accident" involving debt-strapped Greece.
El-Erian pegged the chances of an "accident"—in which Greek and European officials loose the ability to control Greece's future—at 55 percent to 60 percent, which he said was higher than what he had predicted just a few weeks ago.
Greece has come under renewed pressure this week that the country could be on the verge of quitting in the euro zone, after the country's interior minister, Nikos Voutsis, threatened over the weekend to default on loan repayments due to the International Monetary Fund (IMF).
Voutsis claimed the EU and IMF were pushing Greece to make unfair concessions in current bailout talks, without which some 7.2 billion euros ($7.87 billion) of aid frozen since last year would not be released, funds which Greece desperately needs to foot its bills.
But outspoken Greek finance minister Yanis Varoufakis tried to soothe fears late on Tuesday, dismissing previous comments on missing the deadline, adding that he was confident that the country will have reached an agreement with its creditors in early June.
Athens' next tranche of debt is a payment of 300 million euros ($326 million) to the International Monetary Fund, with a total of 1.6 billion euros owed to the fund in early June.
Read MoreVaroufakis battles 'divorce lawyer' style austerity talks
Greece's left-leaning government, led by Prime Minister Alexis Tsipras, has put forward new proposals for its budget to the IMF, with key sticking points in negotiations including pensions and sales tax.
Lew said while there had been progress in the debt talks, it was not enough for the issue to be resolved.
"I don't think anyone wants this to blow up. What I worry about is the accident. You have moments that come about at all too much frequency where just a miscalculation could lead to the crisis that would be potentially very damaging," Lew said.
"I think brinkmanship is a dangerous thing when it only takes one accident. I think everyone needs to double down and treat the next deadline as if it's the last deadline and get this resolved. The risk of going from deadline to deadline only increases the risk of an exit," said Lew.