How many lace bugs can a lacewing eat, when a lacewing is eating lace bugs?

The answer should be known later this summer when laboratory tests being conducted for the National Park Service are complete.

Last week a handful of green lacewing eggs were scattered on azalea bushes at the Lyndon Baines Johnson Memorial Grove, opposite the Pentagon, in hopes they will hatch and eat large quantities of lace bugs, which are damaging azaleas in the grove.

The lacewing experiment is being conducted by California's John Muir Institute, which has been hired by the Park Service to find environmentally safe methods of combating pests on the 55,000 acres of federal parkland around Washington.

Next on the institute's hit list are yellow jackets at Great Falls Park, rats in District parks, mosquitoes on the C&O Canal, flies at Park Service stables and Japanese beetles around the cherry trees at the Tidal Basin.

Until now, the Park Service has relied on chemical warfare to control most pests.

The Muir Institute, whose three-year contract with the Park Service began last summer, doesn't totally reject use of pesticides but stresses natural control of pests, primarily by importing natural enemies, even bacteria, to combat large pest populations.

Last week, institute workes sprayed cherry trees on Hains Point with neem oil, an extract from an Indian tree which repels Japanese beetles and other insects that attack the cherry trees. This fall the institute plans to spray grassy areas near the cherry trees with milky spore, a bacteria that kills Japanese beetle grubs which grow in the grass.

An experiment to control yellow jackets at Great Falls will begin later this summer, where traps, probably baited with Hawiian Punch, will be used to lure the sugar-loving wasps away from the picnic areas, according to Kevin Hackett, Muir Institute coordinator here.

Stable flies will be caught and killed with fly traps and old-fashioned (nonpesticide) fly strips in an experiment at the U.S. Park Police stable beside the Reflecting Pool.

And mosquito-breeding pools in stagnant western sections of the C&O Canal near Cumberland, Md., wll be drained to kill mosquito larvae.

Not all local pests will be easily controlled by natural means. Hardy city rats, which have burrowed networks of underground tunnels around most parks and downtown buildings and ignore poisoned baits, present a problem, admits Hackett.

"But we're studying it. We might try tear gas in their holes, putting in plants that rats don't like . . . but we won't be using ferrets or snakes. They're natural enemies we won't be using."