Will L.A.'s thirst drain continent's oldest lake?

California's Mono Lake, said to be the oldest continually existing lake in North America, is desperately in need of an infusion of fresh water.

So desperate, in fact, that on May 3 the Mono Lake Committee - devoted to the preservation of this unusual body of water - asked the City of Los Angeles to voluntarily reduce its diversion of water from streams that once fed the lake.

As of the end of the week, the committee's letter to City Council president Joel Wachs was, according to an aide, being held pending his return from a trip to China. Mayor Tom Bradley is campaigning for governor, and his office staff did not respond to calls about the Mono situation.

But, as one source noted, in matters of water policy, city officials traditionally defer to the Los Angeles Department of Water and Power (DWP).

The DWP has given no indication of decreasing its use of water from the Mono Lake basin - now amounting to almost the entire flow from the lake-feeding streams. First begun in 1940, diversion of Mono water to the city 300 miles southwest has caused the level of Mono Lake to drop 46 feet. With little or no replenishment of fresh water, the complex ecosystem of the lake is headed at an increasing pace toward ruin.

''The lake's California gull colony, the state's largest, may again face starvation if their food, tiny brine shrimp, does not increase in numbers soon, '' says Ed Grosswiler, executive director of the Mono Lake Committee.

Last spring thousands of gull chicks starved when the brine shrimp population , apparently because of increased lake salinity, dropped sharply. This spring, say scientists studying the lake, there are likely to be even fewer shrimps.

Adds Mr. Grosswiler: ''In view of the heavy snowpack and abundant water supplies throughout the state, the city could reduce diversions and prevent further environmental deterioration at the lake withoutel3l

impact on the city's water supply.''

On the same day the committee's letters went to Los Angeles, lawyers for the National Audubon Society were asking the California Supreme Court, at a San Francisco hearing, to rule that the ''doctrine of public trust'' - under which the state has final power over navigable California waters - applies to permits that enable Los Angeles to divert water from the Mono basin.

DWP lawyers argue that state water laws give the city's needs priority and that the doctrine should not apply in this case.

The water agency holds that there is no immediate threat to the lake, that diversion would be too costly, and that Los Angeles, which gets some 20 percent of its water from the Mono basin, cannot conserve enough to permit release of more water into the lake.

If the California high court rules that ''public trust'' does apply, then the Mono Lake advocates can seek a US District Court ruling in a suit first brought against Los Angeles in state court in 1980.

But the ruling is not expected before the end of the summer, and already it appears too late to avoid the loss of another generation of gulls at Mono Lake.

A bill that would designate Mono Lake as a national monument will be given a hearing May 18 in Washington by a subcommittee of the US House Committee on Interior and Insular Affairs. HR 5424, introduced by US Rep. Norman D. Shumway (R) of Stockton, Calif., would not prevent diversion of water to Los Angeles.

But its backers feel that by giving monument status to the lake it would help their effort to preserve the unique inland sea with its endangered wildlife and spectacular scenery.

Thus, the battle over Mono Lake continues - alongside the ancient and apparently hopeless fight over diversion of Owens Valley water to Los Angeles and the hotly contested state referendum, June 8, on building a ''peripheral canal'' to make more Sacramento River water available to California's ''dry half.''