The Virginia Board of Conservation and Economic Development granted conditional approval yesterday of a 503-acre park in Prince William County that contains the site of the home of Robert E. Lee's grandfather on the Potomac River.

The tract on Freestone Point about five miles south of Woodbridge was offered to the state at half price by its owners, the American-Hawaiian Steamship Corp. The value of the park is to be determined by an appraisal.

If finally approved, the Freestone Point park would be the second state park in Northern Virginia. Development of an 1,800 acre site on Mason Neck in Southern Fairfax County is expected to begin next year using money approved in the Nov. 8 bond referendum.

The acquisition of the park land is contingent or approval by the Prince William County Board of Supervisiors and the appropriation of about $99,000 for maintenance by the General Assembly. It also depends on the availability of federal matching funds to complete the purchase. The land was appraised in 1974 at $2.6 million.

The half-price offer of the land by American-Hawaiian is critical to the acquisition. Virginia can claim the gift portion of its share when it applies for matching funds from the federal government.

The other half of the money, provided through the U.S. Department of Interior, would be paid to American-Hawaiian, which is owned by Daniel K. Ludwig, one of America's richest men. The corporation also would receive a tax break for the gift.

The park would not be developed for at least several years after acquisition, according to state officials.

It eventually would contain a wide mix of activities including nature trails and picnic areas, historical descriptions of the Lee site and swimming and water sports on the Potomac Beach.

The full cost of development would be about $5 million and annual operating costs would run about $150,000, officials said.

While work on the Mason Neck Park will begin as soon as bond money becomes available, the park is not expected to be open to the public until at least 1980, officials said.

About $1.1 million will be available from the statewide bond package while total development costs at Mason Neck will run to about $3 or $4 million.

Northern Virginia's other state park, the Mason Neck Park contains a bald eagle nesting area. It will be devoted to outdoor activities, such as hiking, biking and nature trails. The park will be able to handle about l,000 to 8,000 visitors on a peak day. Present plans do not include sports like golf, tennis or swimming, officials said.

The park is close to and will complement historic Gunston Hall, the home of George Mason, the author of the Virginia Declaration of Rights on which the U.S. Bill of Rights is based.

It also is near a national wildlife refuge and a Northern Virginia regional park that provides facilities for active sports, state officials said.

The Mason Neck Park was purchased in several separate pieces during the late 1960s when Virginia was attempting to acquire land in critical growth areas.

State officials said the decision to buy park land then was made with the knowledge that money might not be available for development for a decade.