In the summer of 1986, IRS auditors in the United States and their counterparts in the U.S. Virgin Islands were deep into independent investigations of a Caribbean-based company that had avoided payment of millions of dollars in income taxes.

The company, called La Isla Virgen Inc., was the creation of a politically well-connected California millionaire, William M. Lansdale. In fact, in March of that year, Lansdale and his wife, Marianthi, had attended a White House state dinner for Canadian Prime Minister Brian Mulroney.

In May 1986, the Virgin Islands Bureau of Internal Revenue issued a deficiency notice, claiming that La Isla Virgen owed $4.5 million in unpaid income taxes and penalties for 1982 and 1983.

Three months later, in August, the Internal Revenue Service, as part of its own wide-ranging audit, issued summonses for "all books, records, contracts, documents and workpapers which were used to determine the income and expenses of La Isla Virgen Inc. for the periods of 1981 through 1986 . . . "

The agencies were moving to close a loophole in U.S. and Virgin Islands tax laws that the company had used to shelter income earned in the United States

from being taxed in either place.

As it turned out, though, there was no cause for concern on the part of Lansdale.

While tax investigators were bearing down on La Isla Virgen, Lansdale, or someone on his behalf, was bearing down on Capitol Hill.

The same month that the IRS issued its summonses, Sen. Bob Packwood (R., Ore.) and Rep. Dan Rostenkowski (D., Ill.), the chairmen of Congress' powerful tax-writing committees, approved a special tax dispensation that absolved La Isla Virgen from paying back taxes.

The tax concession - arranged by a friendly colleague whom they refused to identify - was then incorporated in the Tax Reform Act of 1986, which was passed by Congress in September of that year and signed into law by the President the next month.

Of the dozens of American companies that had taken advantage of the Virgin Islands loophole, only two managed to secure a private law from Congress waiving taxes owed. One was La Isla Virgen.

The other was Bizcap Inc., a company controlled by a millionaire businessman in Dallas who is a contributor to, and supporter of, conservative candidates and causes, including President Reagan's Star Wars defense system.

But, for Lansdale, once was not enough.

The following year, sometime in the summer or fall of 1987, Lansdale's La Isla Virgen, seeking to build on its earlier success, went after its second custom-tailored tax break.

With the assistance once again of a sympathetic congressman, Capitol Hill's tax-law writers drafted yet another provision excusing La Isla Virgen from the payment of income taxes.

That provision, along with scores like it, is waiting to be spliced into technical-corrections legislation that Congress is expected to take up in coming weeks.

About the same time that Capitol Hill tax writers were wrapping up work on drafting Lansdale's second tax preference, President Reagan appointed Lansdale's wife to the National Advisory Council on Women's Educational Programs.

In making the appointment, the White House took note of Marianthi Lansdale's business background, pointing out that since 1961 she has been ''vice president of the Lansdale Co. and president of Marina Pacifica Oil Co. in Seal Beach, Calif."

As was the case with the 1986 tax concession, the pending one is written in a way that conceals the identity of the beneficiary. It says that a company will be excused from paying taxes that others will be obliged to pay if it satisfies certain narrow requirements:

In the case of any pre-1987 open year, neither the United States nor the Virgin Islands shall impose an income tax on non-Virgin Island source income derived from transactions described in clause (ii) by one or more corporations which were formed in Delaware on or about March 6, 1981, and which have owned one or more office buildings in St. Thomas, United States Virgin Islands, for at least five years before enactment of this Act. Each such corporation shall be considered an inhabitant of the Virgin Islands . . .