New York's normally fraternal order of Republicans plunged their convention into unprecedented, downright Democratic fratricide this week, in a beat-the-establishment gubernatorial battle that will carry into a bitter September primary.

Two survived: conservative drug store multimillionaire Lewis Lehrman, who spent almost $3 million on television ads to impress several hundred delegates, and former U.S. attorney Paul Curran, who is the moderate New York Republican establishment's hope of stopping Lehrman. They promptly embarked yesterday on a campaign to out-tough-talk each other, and the Democratic front-runner for governor, Mayor Edward I. Koch of New York City.

"Our streets before our very eyes are turned into hunting grounds of killers and muggers," said Lehrman, who came to the state convention nervous about getting the 25 percent vote he needed to be on the fall primary ballot and wound up getting 68.9 percent and the party's official designation as its candidate for governor.

" . . . Our homes are invaded by faithless barbarians. Our police are used for target practice. . . . What do you say about a city Koch's city that has over 1,800 murders in one year?" The death penalty, Lehrman answered, is what New York needs.

Curran, who had hoped the establishmentarians could deliver a majority of the delegates for him but wound up with just 31.1 percent, criticized Koch and pined for the Republican Party of yesteryear "that could throw the rascals out and make sure criminals went to the slammer." The death penalty, he promised, "will be law, I guarantee you, right after I become governor."

Then Curran went on to set the tone for the primary campaign to come by raising thinly disguised questions about the honesty of Lehrman's past claims of personal achievement and his ability to withstand future political assaults.

New Yorkers will be treated in the fall to two primary battles heavy with ideological overtones.

Lehrman will present his credentials as a Reagan Republican, an early supply-side adviser to the Reagan team who sought to become secretary of the Treasury.

Curran has the solid backing of the party moderates, the Rockefeller Republicans. He headed the federal inquiry into the financing of a peanut warehouse owned by then-president Carter.

The Democratic primary will feature Koch, a one-time liberal congressman who has won New York popularity with his acerbic quips and neo-conservative lines, against Lt. Gov. Mario Cuomo, who is more contemplative and liberal. Koch was once thought to have the gubernatorial nomination sealed, but Cuomo has closed to within 10 points according to the latest poll by Gannett newspapers.

Lehrman also is almost certain to be nominated for governor by the Conservative Party and Cuomo is likely to get the Liberal Party nomination. Thus, they will be around in November, even if they lose their major-party primary contests, to siphon votes away from their respective conquerers.

This past week proved to be a new experience for New York's Grand Old Party.

For decades, the state's Republicans had come by their candidates for governor by a sort of political Immaculate Conception, with the GOP elder statesmen merely agreeing on their standard-bearer.

But this time four candidates laid claim to the nomination: Lehrman, Curran, Assembly minority leader James Emery and former state party chairman Richard Rosenbaum.

Finally late Wednesday night, after day-long balloting and futility, Emery withdrew in the name of party unity, and then Rosenbaum followed suit--and the convention returned the favor by designating Emery by acclamation as its candidate for lieutenant governor.

Amost all the released delegates switched to Lehrman--to the surprise of the moderate party leaders and of Lehrman as well.

Three candidates got the required 25 percent of the delegates to qualify for the ballot in the U.S. Senate primary: former U.S. attorney Whitney North Seymour, former state banking superviser Muriel Siebert and Brooklyn assemblywoman Florence Sullivan. The winner will have an uphill battle against Democratic incumbent Daniel Patrick Moynihan.

The convention ended with a hastily arranged drop-in by President Reagan, who was in town to address the United Nations.