LOS ANGELES (AP) _ Actress Lynn Redgrave will appeal a $10 million lawsuit brought against Universal Television, which she says fired her for breast-feeding her baby on the filming set, her attorney said.

''We will absolutely appeal,'' Peter diDonato said Tuesday, after a judge refused to hold a new trial.

Miss Redgrave claimed she was wrongly fired from the CBS television show ''House Calls'' because she wanted to breast-feed her daughter, Annabel, on the set.

Superior Court Judge Jack Ryburn ruled that the case filed in 1983 had been settled verbally in June 1986 by the actress' husband and manager, John Clark, and Universal President Robert Harris.

Miss Redgrave and Clark contend there was no settlement because neither of them signed an agreement, diDonato said. The agreement calls for Universal to apologize publicly and pay $100,000 in attorney fees.

---

NASHVILLE, Tenn. (AP) - Country music star Johnny Cash, who was hospitalized for exhaustion, plans to rest at home for about 10 days before picking up his guitar again.

''He hopes to resume performing May 30 in Memphis,'' Cash's manager, Lew Robbins said Tuesday. ''He's better but tired.''

The 55-year-old singer, known for such hits as ''A Boy Named Sue,'' and ''Ring of Fire,'' fell ill during a concert Saturday in Council Bluffs, Iowa. He was hospitalized there for two days and returned home Monday.

---

PROVIDENCE, R.I. (AP) - Children's author Theodor ''Dr. Seuss'' Geisel, musician Stevie Wonder, and television journalist Connie Chung will receive honorary degrees from Brown University.

Geisel, whose classics include ''The Cat in the Hat'' and ''Green Eggs and Ham,'' will be among eight honorees at commencement ceremonies Monday, the school said.

The date is the 50th anniversary of the publication of Dr. Seuss's first children's book, ''And to Think That I Saw It on Mulberry Street.''

Also receiving honorary degrees will be Portugal's president, Mario Soares; Joan Ganz Cooney, president of Children's Television Workshop; publisher and businessman Earl Graves; Fabio Roversi Monaco, head of the University of Bologna in Italy; and archaeologist Joseph Shaw.

---

WASHINGTON (AP) - Sen. Brock Adams, D-Wash., a transportation secretary under President Jimmy Carter, is nursing a broken elbow after a fall in the ''Smash-In'' charity tennis tournament.

''I'd love to say it happened as I was making a dramatic lunge at the net, but it was a simple accident,'' the freshman senator said. ''I ran back for a lob. My partner ran into me and I ran into the court.''

Adams is telling people his fall at the tournament here last weekend makes him the latest victim of ''disarmament,'' his deputy press secretary Emily Love said.

---

NEW YORK (AP) - Sir Georg Solti, the Grammy Award king and the Chicago Symphony's music director, has belatedly received his latest Grammy at newly- renovated Carnegie Hall, which he says sounds better than ever.

Sir Georg, who missed the awards ceremony in Los Angeles, accepted his 26th Grammy on Tuesday night for Liszt's ''A Faust Symphony,'' which won in the category of best classical orchestral recording.

The Chicago Symphony performed at Carnegie Hall on Monday night for the first time since the hall reopened last spring after extensive renovations.

''It didn't lose the beauty or articulation of the sound,'' Sir Georg said. Sir Georg has won more Grammies than any other musician. Henry Mancini is second with 20.

---

LOS ANGELES (AP) - Lucille Ball was ''devastated'' by the failure of her latest TV show, says her daughter, actress Lucie Arnaz, who is making a TV movie about her father, the late Desi Arnaz.

The comic actress ''felt terrible'' after ''Life With Lucy,'' was canceled, Miss Arnaz said. ''It really devastated her. She's terrified to go back.''

Miss Arnaz, co-starring in the play ''Social Security'' with her husband, Laurence Luckinbill, says she would like to persuade Miss Ball to perform with her in a movie version of the comedy about an aging mother's rediscovery of passion.

The play runs through June 20 in Los Angeles, then moves to San Francisco.

Miss Arnaz and Luckinbill are co-producing ''The Desi Arnaz Story,'' based on the autobiography of her father, the actor-bandleader who co-starred with Miss Ball in ''I Love Lucy'' and co-founded Desilu Studios.

Miss Arnaz said she has considered her brother, Desi Arnaz Jr., for the lead in the CBS movie.