Leonard "Lennie" Niehaus was born on June 1, 1929, in St. Louis, Missouri, the son of Aaron Niehaus, a Russian-born violinist who played in the orchestras that accompanied silent films. When talking pictures emptied the theater pits, the family moved to Los Angeles in the mid-1930s and his father found work in the Hollywood studio orchestras; his sister Agnes became a concert pianist. Niehaus began on violin at seven, played oboe and bassoon in school, and took up the alto saxophone and clarinet at thirteen. He later recalled hearing Charlie Parker at Billy Berg's in 1945 and being "blown away" by bebop. While still at Roosevelt High School he was the lead alto and arranger in the band of Phil Carreón, whose saxophone section included Herb Geller, Herbie Steward and Teddy Edwards, and which at different times also held Warne Marsh and the trombonist Jimmy Knepper. He studied at Los Angeles City College from 1946, alongside the future trumpeter Jack Sheldon and the tenor saxophonist Jack Montrose, and earned a music education degree at Los Angeles State College in 1951.

His professional break came with the Stan Kenton orchestra. Recommended to Kenton in the early 1950s as a replacement for Art Pepper, he auditioned by sight-reading Gerry Mulligan's "Limelight" and was hired, but after about six months on the road he was drafted in 1952 and served until 1954 at Fort Ord, California, in the 6th Infantry Division Band. There he met a fellow soldier, Clint Eastwood, and the two bonded over jazz; in his off hours Niehaus sat in with Shorty Rogers' Giants and Howard Rumsey's Lighthouse All-Stars. After his discharge he rejoined Kenton in 1954, taking the lead alto chair that Lee Konitz had just left, and stayed until 1959, the longest and most-recorded tenure of any of the band's lead altos. He soloed on albums including Contemporary Concepts (1955), Kenton in Hi-Fi (1956), Cuban Fire!, Rendezvous with Kenton and Back to Balboa (both 1958), and the 1959 Kenton Live from the Las Vegas Tropicana, toured Europe with the band in 1956, and was named Down Beat's New Star on alto saxophone in 1955. As a writer he supplied Kenton with charts throughout the decade, among them the whole of The Stage Door Swings (1958), which he wrote in about two and a half weeks, and later Sophisticated Approach and Adventures in Standards (both 1961), after he had stopped playing in the band.

Alongside the Kenton job he led his own records for Les Koenig's Contemporary label, on the advice of Shelly Manne. The first, a pianoless quintet date recorded in July 1954 with Jack Montrose, Bob Gordon, Monty Budwig and Manne, voiced three saxophones so that they sounded like six. An octet followed on August 23, 1954, with Lou Levy, Stu Williamson and Bob Enevoldsen; a second octet with Jimmy Giuffre and Bill Holman in early 1955; The Quintets and Strings in March and April 1955, which wrote a viola and cello quartet into the horn lines as if it were a sax section, with Hampton Hawes and Bill Perkins among the players; and The Sextet in January 1956. A further octet session on December 10, 1956, with Pepper Adams, Frank Rosolino and Red Mitchell, was later paired with the 1954 octet on Zounds! (1958), and he made one date for EmArcy, I Swing for You (1957). In the same years he arranged and played on records for others, including Duane Tatro's Jazz for Moderns and the Hollywood Saxophone Quartet.

In 1959 he gave up full-time playing to write, and from then on his working life was mainly in film and television. He wrote for the King Sisters, Mel Tormé, Dean Martin and Carol Burnett, and from 1962 orchestrated for the composer Jerry Fielding on about seventy television shows and films, among them Hogan's Heroes, Straw Dogs, The Bad News Bears, The Outlaw Josey Wales and Escape from Alcatraz. After Fielding's death in 1980 he became Eastwood's regular composer, writing the full score for Pale Rider (1985) and twelve more of Eastwood's films through Blood Work (2002), among them Heartbreak Ridge, Unforgiven, A Perfect World, The Bridges of Madison County and Space Cowboys, and orchestrating Eastwood's later films from Mystic River (2003) to Gran Torino (2008). His score for Bird (1988), Eastwood's film about Charlie Parker, was nominated for a BAFTA Award, and he coached the actor Forest Whitaker to look convincing playing the saxophone. He won a Primetime Emmy for the 1993 Showtime film Lush Life, in which Whitaker again played a jazz saxophonist, and was nominated again in 2008 for Mitch Albom's For One More Day. In the 1970s he published the method book Jazz Conception for Saxophone, followed by further educational volumes and saxophone ensemble pieces.

After many years away from the saxophone he returned to playing and recording in his sixties, leading a quintet with Frank Strazzeri, Bill Perkins and others on Patterns (recorded 1989), reuniting with Perkins and Jack Nimitz on Seems Like Old Times (recorded December 1997), and recording the live Live at Capozzoli's (October 1999) and, with an octet, Sunday Afternoons at the Lighthouse Cafe, Hermosa Beach (October 2004). He spent his last years playing with Los Angeles jazz groups. Niehaus passed away on May 28, 2020, at the age of 90, at his daughter's home in Redlands, California, under hospice care. He was survived by his wife, Patricia, his daughter Susan, and his grandchildren.

Niehaus played alto with a cool, clean tone and fast, flowing lines that came out of Charlie Parker and Lee Konitz, the two players he named as his main models; he also credited Benny Carter, Phil Woods, Joe Maini, Cannonball Adderley and Sonny Criss. He was best known as a writer of West Coast linear jazz, a contrapuntal approach he said grew from counterpoint studies in college: his small-group charts spread the horns in open voicings so that a quintet or octet sounded larger, and on The Quintets and Strings he wrote the strings as independent melodic lines, in the way a saxophone section would be handled, rather than as accompaniment. His Kenton arrangements moved that band toward more interplay between sections and a stronger reed voice. AllMusic singles out his Contemporary quintet and sextet albums, and the critic Marc Myers calls his mid-1950s small-group records the place to hear his musical gifts at full strength. He is also known to a much wider audience as a film and television composer, and AllMusic files him under both Jazz and Stage & Screen; his scores often kept a jazz base, as in the 1930s-style music for City Heat (1984), which used players such as Marshal Royal and Bill Perkins, and the Parker-centered score for Bird. His jazz recording is concentrated in two periods, roughly 1954 to 1959 and again from 1989 onward, with his film and television work filling the decades between.