Justice Anthony M. Kennedy, the greatest judicial champion of gay rights in the nation’s history, will turn 81 on Sunday. Rumors that he would retire in June turned out to be wrong, but he will not be on the Supreme Court forever.

Gay rights groups hope to score one more victory before he leaves the court. The goal this time is nationwide protection against employment discrimination.

Justice Kennedy wrote the majority opinions in all four of the court’s landmark gay rights rulings, culminating in the 2015 decision establishing a constitutional right to same-sex marriage. But there is more work to be done, said Suzanne B. Goldberg, a law professor at Columbia.

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“Marriage equality did not bring an end to sexual-orientation discrimination in this country,” she said.

The same-sex marriage decision left gay men and lesbians in a strange position, said David S. Cohen, a law professor at Drexel University.

“You can get married, put a picture on your desk from the wedding and then be fired because the boss sees the picture,” he said.

“Marriage was certainly an important step, but it doesn’t change the fact that there is no federal law protecting against sexual-orientation discrimination in employment or housing or education or public accommodations,” Professor Cohen said. “Only about 20 states offer protection under their own state laws.”

This month, the gay rights group Lambda Legal announced that it would ask the Supreme Court to hear a case that could prohibit employers from discriminating against gay and lesbian workers. The group argues that Title VII of the Civil Rights Act of 1964, which prohibits workplace discrimination based on sex, also bans discrimination based on sexual orientation.

Most federal appeals courts have rejected the theory. But in April, by an 8-to-3 vote, the United States Court of Appeals for the Seventh Circuit, in Chicago, said Title VII covered gay people. “It would require considerable calisthenics to remove the ‘sex’ from ‘sexual orientation,’” Chief Judge Diane Wood wrote for the majority.

She relied on the language and logic of Title VII, and on Supreme Court precedents.

In 1989, for instance, the Supreme Court said discrimination against workers because they did not conform to gender stereotypes was a form of sex discrimination. Being a lesbian, Judge Wood wrote, “represents the ultimate case of failure to conform to the female stereotype (at least as understood in a place such as modern America, which views heterosexuality as the norm and other forms of sexuality as exceptional).”

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In dissent, Judge Diane S. Sykes said the majority had overreached. “It’s understandable that the court is impatient to protect lesbians and gay men from workplace discrimination without waiting for Congress to act,” she wrote. “Legislative change is arduous and can be slow to come. But we’re not authorized to amend Title VII by interpretation.”

The Seventh Circuit’s ruling in April created a split among the federal appeals courts, and such disagreements often prompt the Supreme Court to step in. But the defendant in the case, an Indiana community college, quickly announced that it would not appeal.

Legal experts said it was only a matter of time until the Supreme Court addressed the issue.

“The odds that the Supreme Court grants review of this question in the near future are high,” Joshua Matz wrote in April on Take Care, a legal blog. “It is no exaggeration to say that Title VII’s application to gays and lesbians now ranks among the most important open questions in U.S. civil rights law.”

The next case is now on the horizon. It concerns Jameka Evans, who says a Georgia hospital discriminated against her because she is a lesbian. In March, a divided three-judge panel of the 11th Circuit, in Atlanta, ruled that Title VII did not cover discrimination based on sexual orientation.

Gregory R. Nevins, a lawyer with Lambda Legal who represents Ms. Evans, chose his words carefully in discussing whether the odds of winning at the Supreme Court would dim if Justice Kennedy retired.

“We think we have good reasons for optimism with the current composition of the court,” he said. “You always want the setup that you feel comfortable with, rather than any variation of it.”

“Justice Kennedy has viewed the mistreatment of lesbian, gay and bisexual individuals with a jaundiced eye,” Mr. Nevis added.

Legal scholars were more direct. “Kennedy is more sympathetic to gay rights than his replacement is likely to be,” said Andrew M. Koppelman, a law professor at Northwestern who wrote a 1994 law review article called “Why Discrimination Against Lesbians and Gay Men Is Sex Discrimination.”

Professor Cohen, who agreed that Title VII should be read to cover sexual-orientation discrimination, said there was reason for gay rights groups to move quickly. “Certainly anything trying to protect people from discrimination in any form is going to fare better with Justice Kennedy on the court than with another Trump appointee,” he said, “although I certainly don’t think it’s a slam dunk with Justice Kennedy.”

Justice Kennedy has never embraced the theory that sexual-orientation discrimination is a form of sex discrimination. But he seemed intrigued by the question in 2013 when the Supreme Court heard arguments about Proposition 8, a referendum that banned same-sex marriage in California.

“Do you believe this can be treated as a gender-based classification?” Justice Kennedy asked a lawyer defending the ban.

He did not wait for an answer. “It’s a difficult question,” Justice Kennedy said. “I’ve been trying to wrestle with it.”