Virginia State Sen. L. Douglas Wilder of Richmond expects to raise only $500,000 in his Democratic campaign for lieutenant governor, about half of the goal he set for himself last year when he announced, a campaign official said today.

Paul Goldman, Wilder's chief campaign consultant, said the Richmond state senator "has not received the money from our traditional Democratic sources. It's difficult to raise money when you are the underdog." Asked who was not contributing as expected, Goldman singled out organized labor, which endorsed Wilder last fall.

Wilder also doesn't expect to raise enough money for potentially crucial television advertisements, Goldman said. "Basically, we're hopeful people will cover us," said Goldman.

Goldman insisted the campaign has always expected to raise about $500,000. In his announcement a year ago, Wilder told reporters his budget would be between $750,000 and $1 million.

Wilder's opponent, Republican State Sen. John H. Chichester of Fredericksburg, has said that he expects $1 million to be spent on his campaign. But Chichester's campaign manager, Dennis Petersen, said that figure includes both joint campaign efforts with the other Republican candidates and donated services. Petersen declined today to say how much the campaign will raise in cash.

The money either candidate raises could play a crucial role in the final weeks of the Nov. 5 general election, when expensive media advertising could affect the outcome.

"It's a traditional Democratic approach to cast themselves as the underdog," Petersen said. He said Wilder, who is expected to release a finance report on Monday showing that he has about $200,000, had $85,000 in cash a month ago, while Chichester had less than $20,000 in cash on hand.

Meanwhile today, Virginia Republican Sen. John W. Warner briefly crossed party lines to defend Wilder's tactic of promoting his Korean War record in the campaign for lieutenant governor.

"I felt it was important for me to rise above any political considerations," Warner said in a telephone conversation.

Wilder, a Richmond lawyer, was criticized last week by the president of a Northern Virginia Chinese American group for campaign literature that reads, "From Korea to Richmond, He's Still Fighting for Virginia." Wilder won a Bronze Star in the Korean War.

James Tso, president of the local chapter of the Organization of Chinese Americans, complained in a newsletter that the phrase might heighten racial tensions between blacks and Asian Americans. Tso said it is "particularly sensitive in Northern Virginia where black American and Asian American relations are going through a period of suspicion, envy and sometimes outright contention . . . . "

Warner, stressing his support for Republican Chichester, said it was "proper" for Wilder to refer to his service record. Warner, who served in both World War II and Korea, is a former secretary of the Navy.

Warner offered in his letter to Tso to meet with him and others over racial problems.

In addition to Warner, who telephoned Wilder this week and sent a letter to Tso, Wilder also received a telephone call from Sen. Warren B. Rudman (R-N.H.), who was an Army infantry captain during 1952-54. Fourteen Virginia state senators also signed a statement praising Wilder. CAPTION: Pictures 1 and 2, L. Douglas Wilder . . . expects to raise about $500,000; John W. Warner . . . crossed party line on war record.