THE UNIQUITOUS LILY - There is a whole society dedicated to growing the perfect lily, and from 1 to 5 Saturday and 10 to 5 Sunday you can see the best of the best at the National Arboretum. Go to the Auditorium of the Administration Building, at Bladensburg Road and R Street NE, where the Potomac Lily Society will be sponsoring its 20th annual show. Admission is free. Call 526-2447.

PICNIC WITH MR. WILSON - The gardens of the Woodrow Wilson House, where the President spent his last years, are open to the public on Sunday, noon to 5, for $2 (75 cents for students). Bring your own lunch; then, for dessert, sample the lemonade, cookies and homemade ice cream that will be available, and listen to the madrigals.

Wilson's White House and World War I momentos fill the townhouse at 2340 S Street NW - the only former presidential home in town that's open to the public (the White House doesn't count). You can also see a special exhibit there on, of all things, professional baseball in The Nation's Capital. For information, call 387-4062.

TENDING TREES - There's more to trees than climbing them. Wednesday evening at 8:30, a naturalist at Burke Lake Park, 7315 Ox Road (five miles south of the City of Fairfax), will hand out advice on how to transport, plant, fertilize and prune trees. The program focuses on trees native to this area. Call 451-9588.

THE DISAPPEARING ORCHID - Orchids don't thrive in shopping-center parking lots, so they are losing their habitats to "progress." Now through July 15 a photography exhibit at the National Museum of Natural History captures the beauty of native orchids. The National Capital Orchid Society assembled the exhibit of 27 color photographs of the flowers, which now grow almost exclusively in outlying parks and along the C&O Canal.

Bronzes by Jean Ann Whiteman of African wildlife also grace rotunda gallery of the museum at 10th Street and Constitution Avenue NW.