Metro, disturbed that it is losing an almost effortless $95,000 a year because Congress has ruled that lottery ads are unfit for the subways and buses of the nation's capital, is launching a low-key campaign to change their minds.

At issue is language inserted in the 1982 D.C. Appropriations Bill to mollify skeptics who opposed creation of the D.C. Lottery. It specifically outlawed lottery ads on Metro on the grounds that they might offend transit-riding tourists and out-of-towners here on business.

That limitation's prime defender is Rep. Lawrence Coughlin (R-Pa.), ranking Republican member of the House D.C. appropriations subcommittee. In an editorial on Channel 4 television this summer, Coughlin argued that, like it or not, D.C. belongs to all Americans, not just the people who live there.

"A profusion of lottery signs in this city of national shrines would cheapen the nation's capital in the eyes of millions of Americans who consider the District of Columbia their city too," Coughlin said.

The law also bans sale of lottery tickets in "Historic Georgetown," the federal enclave near the Mall and other federal sites.

In a letter to subcommittee Chairman Julian C. Dixon (D-Calif.), Metro General Manager Richard S. Page urged repeal of the advertising ban, saying that "transit advertising of the lottery would substantially increase revenues and thereby lower subsidy requirements." Subsidies are scheduled to total about $177 million this year.

In fact, Metro has already signed a contract with the lottery under which 360 signs would displayed around town on the backs ofMetrobuses--all contingent on removal of the pertinent language.

It would be one of Metro's largest ad contracts, netting it $95,000 a year, or about 5 percent of the $2 million Page says Metro makes from advertising yearly.

Metro officials suggest the ban is particularly unfair in light of Reagan administration programs to reduce federal aid and force transit systems to be more self-reliant.

About 350,000 people ride Metro's buses and trains on an average weekday. About 4 to 5 percent of them live outside D.C. and the seven suburban jurisdictions in the transit system, according to ridership surveys.

Assisting Metro on the Hill is the Transit Advertisers Association, which hopes to win business for National Transit Advertising, Metro's ad agency. Like Metro, it would stand to earn $95,000 from the contract.

Association counsel William Oldaker argues that due to heavy publicity elsewhere, the ban simply does not serve its purpose of keeping the lottery out of visitors' sight. He says: "It's on TV. It's in the newspapers. There are bumper stickers. The only place where it's not is on Metro."

Opposing forces appear to be stalemated for the present. The Senate version of the 1983 D.C. appropriations bill would lift the ban, but the House version would retain it.