IF LEWIS LEHRMAN somehow were elected to succeed New York Gov. Hugh Carey, the Democratic pols were laughing this summer. New York would be the only state to have had governors Hughie, Dewey, and Lewie. But those same Democratic pols were the ones laughing this summer at the thought that anyone could beat New York Mayor Edward I. Koch in a Democratic gubernatorial primary. They're not laughing anymore.

Lehrman didn't inspire much awe a few months ago. Perhaps second only to Koch himself, Lehrman has the physical air of chicken man Frank Perdue gone Ivy League. Scion of a wealthy family, Lehrman seemed a poor little rich boy with the improbable trademark of a pair of red suspenders--hardly a marketing package designed to sell well in most parts of the state.

But Lehrman saturated the airwaves and took the Republican primary in a romp, reportedly spending more than $6 million of his own money for that initial race alone. By becoming a fixture on daily and night time television, Lehrman has catapulted himself through sheer dollars into a leading spokesman for conservative, indeed libertarian, government. Or, as his Democratic opponent Lt. Gov. Mario Cuomo put it, "a more Radical version of Reaganomics."

Cuomo is everything Lehrman is not. Where Lehrman lives on the upper East Side of Manhattan (now that he lives in Manhattan at all--until five years ago, he lived in Pennsylvania, reportedly to avoid income taxes). Cuomo lives in Queens. He is from the "outer boroughs," the neighborhoods. He's an Italian Catholic. He's well- read.

Cuomo is perhaps the great example nationwide this election year of a candidate trying to revive the old New Deal Coalition. He is the darling of the cosmopolitan liberal intellectuals--as shown this summer when the Village Voice all but deified him weekly. He has unanimous and enthusiastic labor support--in New York's very strong organizational asset. He has strong support from Black and Hispanic voters who know that they have nothing to gain from Lehrman's ledger-book legislation. And he has a clear edge among his own Catholic middle class.

ITALIANS COMPRISE almost one-fourth of New York State, and between Cuomo and his lieutenant governor candidate Alfred Delbello they have a chance to put two of their own into statewide prominence. Cuomo will probably be able to bring increasingly conservative Italian voters back into the coalition it only because of his own ethnicity.

With the ideological dichotomy between the two candidates so clear, the race has seen an unprecedented amount of ethnic campaigning Lehrman is Jewish, while most of the state's Jews are consistently liberal Cuomo is an Italian Catholic, while most of his fellows are much more conservative. The result is a feverish attempt by both candidates to raid the other's ethnic group while holding onto their own.

Cuomo is campaigning hard for the Jewish vote, which he has termed crucial to his success. This fervor indeed led him during the primary campaign against Koch to make the little noticed but really quite remarkable--observation that second only to the family home, his biggest single investment is in Israeli bonds Lehrman has matched this ethnic campaigning.

In many ways this election is just a test case of whether the left or the right is stronger statewide in New York. To the surprise of few, a recent New York Times poll revealed that Cuomo is winning in New York City. Lehrman is winning upstate, and the two are running about even in the suburbs.

Turnout is always crucial for statewide liberals, and the key to success for Cuomo lies in getting his voters to the polls. Lehrman's conservative, lower-taxes, tough-on-crime voters will vote on their own. But there are more New Yorkers a shade to the left than a shade to the right of the political spectrum. Cuomo has every sector of the old New Deal coalition behind him, and that is more than a majority.

New York tends to vote fairly liberal. All the money in the Lehrman family coffers can't change that.