The outgoing president of the University of the District of Columbia, Lisle C. Carter Jr., yesterday urged about 1,000 graduates--most of whom are D.C. residents--to preserve "self rule" in the District and said that their city could lose its home-rule gains if voter turnout here remains low.

Meanwhile, at Howard University's commencement exercises yesterday, Ed Bradley, coeditor of "60 Minutes," challenged 2,000 graduates not to lose hope as they face bleak economic and unemployment forecasts and to make an impact on the world by taking control of their own lives.

Though they spoke on different matters, both men seemed to strike a common chord--a citizen's responsibility to himself as a participant in a democratic society.

At the UDC commencement, held in the courtyard of the Van Ness campus, Carter said, "The people of the District of Columbia are entitled to the form of representative government they want, whether it is statehood, voting representation (in Congress), or greater autonomy within the existing home rule charter structure. But I am certain that we shall have none of them unless we, as District residents in substantial numbers, turn out to support the form of government we want."

Carter, who was keynote speaker, noted that the 1978 mayoral election drew less than one half of all eligible voters and the 1979 school board election only 12 percent.

Carter reminded the audience that Congress had granted limited self rule to the District in the 19th century and then snatched it back 70 years later. He said that the home rule authority the District has won in the last decade could again be lost.

"As citizens of a jurisdiction still trying to demonstrate its hunger for true self rule," he said, "plainly we have to do much better than those residents of other places who tend to take self-government for granted."

Carter, a tall, bespectacled man with a thick mustache and salt and pepper hair, leaves UDC in June to enter private law practice. He was the university's first president and presided over the complex merger of the school's three predecessor institutions--D.C. Teachers College, Federal City College, and the Washington Technical Institute.

Carter, whose speech was interrupted by applause five times, grew emotional near the end when he thanked university officials and students for their help over the past five years.

The mood was solemn during much of Howard University's 114th commencement exercises, held in Howard Stadium and attended by about 15,000 people. Clouds hung overhead throughout the event, threatening to drench caps, gowns and prideful spirits with rain. But jubilation and smiles became infectious as rays of sunshine began to radiate through the clouds just in time for the university's president, Dr. James E. Cheek, to announce the many graduates.

Bradley, who received his first honorary degree at the Howard commencement, told the graduates that the black Americans' struggle for "equality of opportunity" continues. It is no longer a 1960s-type of struggle with the masses united together, he said. It is one being fought on an individual basis.

"You control your life. . . There will be no Moses to lead you to the promised land. At least not on this earth," Bradley said. "If you are to find your way there--to the promised land of equality of opportunity, to the promised land that offers your constitutional rights--you must chart your own course.

"Today all too many are undereducated, miseducated or not educated at all. . . slaves still, in a system based on knowledge and education."

Graduates at both universities were moved by the speeches.

"I thought I was going to hear the same old rhetoric about the downtrodden black man. But he Bradley spoke about self-determination. I was really impressed," said Ronald Jackson, 29, who received a bachelor's degree in criminology from Howard.

Carter's speech struck home for a UDC graduate who received a bachelor's in business management. Marjorie M. Jiles said, "We just can't sit back and not vote and expect the District to do what we want."