Nancy Reagan has hit some pretty high roads in her crusade against drug abuse. Now look for her to hit the high seas at the invitation of Navy Secretary John F. Lehman Jr.

Eager to show off how the Navy wages its war on drugs, Lehman invited the first lady to come aboard and see for herself. She'll do just that on July 17 when Lehman escorts her by helicopter to the USS America, steaming somewhere off the Virginia coast.

Press secretary Jennefer Hirshberg said yesterday that the first lady would meet with some of the 5,000 men aboard, see something of the carrier's flight operations and be briefed on the Navy's drug prevention, control, education and detection programs. The Navy considers urinalysis to be the most effective means of detection and last year 1.8 million officers and enlisted men and women underwent the test.

"The underlying principle in the Navy's war against drugs can be summed up in a single phrase: Zero tolerance," a Navy spokesman said yesterday.

Hirshberg said Mrs. Reagan would spend the night aboard the America, which raises the question of accommodations.

"They might have an acoustical-tile ceiling so you don't see the steam pipes and they might have a picture on the bulkhead," speculated a Navy spokesman about flag officer quarters aboard the America. "Otherwise, they're not particularly plush."