In the 1982 campaign's classic left vs. right battle, New York Democratic gubernatorial nominee Mario Cuomo has surged to a lead apparently strong enough to stave off a late rush by Republican Lew Lehrman.

Cuomo, the liberal lieutenant governor, held a 10-point lead over the advocate of supply-side economics in the New York Daily News straw poll based on statewide interviews between Wednesday and Saturday night. He held a 9-point lead in a statewide poll completed by Newsday a day earlier.

But advisers for both candidates reported that in the last few days, Lehrman has made gains, primarily among undecided voters.

Cuomo's polling, by Patrick Caddell who worked for former president Jimmy Carter, showed figures as of Saturday night that approximate those in the newspaper polls.

But Lehrman's tracking, surveyed for him by President Reagan's pollster, Richard Wirthlin, had Lehrman cutting a 12-point deficit Wednesday to 3 points Saturday night.

Cuomo's advisers still feel confident of victory, and Lehrman's believe that catching Cuomo will be difficult at best.

While national attention has been focused on the candidates' policy differences, strategists for both believe the contest may be decided as much by ethnicity as philosophy.

A key portion of Cuomo's supporters include Italian-American Republicans who have said in surveys that they will vote according to their heritage rather than firm beliefs on fiscal policy and law and order. In the closing days of the campaign, both camps have aimed considerable efforts toward these voters.

The most notable push has been through a $1 million series of ethnically targeted mass mailings by Lehrman, a multimillionaire businessman.

Mailings have been made to Jewish, Irish and Italian voters, with straying Italians being encouraged to return to the GOP fold. "The mailings are just hitting now," said Lehrman's campaign manager, Karl Ottosen.

Added a respected state Democratic strategist: "Mario Cuomo's ethnicity is emerging as an essential reason to vote for him . . . for a key segment of the voters in the state."

Italian Americans make up about one-fourth of the state Republican vote. They are conservative in their politics, yet surveys have shown that about 30 percent of them support Cuomo, according to officials in both camps.

These voters alone could account for several points in Cuomo's statewide totals and, if they turn to Lehrman, the race could be almost even. On the eve of the election, they are the major reason why Lehrman has been unable to amass a lead in the Long Island suburbs that his strategists have repeatedly said are crucial to his chances.

Meanwhile, Cuomo has maintained strong support from Jewish voters, who traditionally vote Democratic. Newsday's poll showed 60 percent of them voting for Cuomo, with just 25 percent for Lehrman, who is Jewish.

Cuomo has scored heavily by recalling for campaign audiences that Lehrman advised Reagan on his supply-side economics program. Wirthlin, realizing that Lehrman's tie to the tax-cutting Reagan was hurting him, advised Lehrman to play down a massive tax-cutting program he had proposed for New York state.

Lehrman started calling it a jobs program instead, making scant mention of the fact that the jobs could be created only because of tax-cut benefits he was proposing for businesses.

Lehrman has also been seen in all surveys of state voters as by far the more inexperienced of the two candidates. Some of his advisers concede that this impression was amplified by his refusal of most invitations to debate Cuomo.

Lehrman's mailings to Italian and Irish voters have emphasized that Cuomo opposes the death penalty, which Lehrman champions in every speech, and they say that Cuomo favors tax-funded abortion and opposes tuition tax credits for private schools and voluntary school prayer.

One Cuomo adviser says the candidate was particularly incensed when Cuomo's 9-year-old son brought home one of the Lehrman Italian mailings handed him in his parochial school by a nun.

The mailing, which carried the name of the state Republican committee, was headlined: "It's time to stop the destruction of our traditional values." The sheet said: "It will still 'pay' to rob, murder and mug if the lieutenant governor becomes governor."

As the Cuomo official tells it, the nun asked Cuomo's son, "Does your dad believe in the traditional family values or not?" as she handed him the mailing.

"That really got to Mario," said his campaign manager, William Haddad. "It is as ethnic a campaign as I've ever seen."