Born in the village of Nainiškiai in the Panevėžys district in 1930, she lives in Vilnius. She is the wife of Algirdas Steponavičius, the graphic artist and children’s book illustrator, and mother of Daina Steponavičiūtė, a graphic artist. She studied graphic art at the Lithuanian State Art Institute, graduating in 1956. She worked as an art teacher at the Vilnius M.K. Čiurlionis Art school from 1963 to 1987, and also made engravings. In 1964, together with Algirdas Steponavičius and Laimutis Ločeris, she painted murals for the Nykštukas children’s cafe in Vilnius. From 1969 to 1972, together with Steponavičius, she decorated the Pušelė children’s sanatorium in Valkininkai with murals. She made her first illustrations for children’s books in 1957; her own original style, combining elements of folk and pop art, evolved around 1964 (the illustrations to Mykolas Sluckis’ children’s book Nedėkingas ančiukas [The Ungrateful Duckling] and to the tales Užburtos birbynės [The Enchanted Pipes] by Sonė Tomarienė).
Žilytė has been considered an innovator since 1967, when the children’s book by the Latvian classic Janis Rainis Aukso sietelis (The Little Golden Sieve) with her illustrations was published. In 1969, she was awarded the Golden Apple for the book at the Bratislava Children’s Book Illustrations Biennial. In 1971, she won the gold medal at the Leipzig Book Fair for her illustrations to Pasaka apie narsią Vilniaus mergaitę ir galvažudį Žaliabarzdį (A Fairy Tale about the Brave Girl from Vilnius and Greenbeard the Killer) by the Lithuanian writer Aldona Liobytė. For this book and Pabėgusi dainelė (The Little Song that Ran Away) by Liobytė, which was published in 1966, she was awarded the State Prize of Soviet Lithuania. In 1976, her illustrations to Kostas Kubilinskas’ Stovi pasakų namelis (A Little Fairy-Tale House) earned her the Hans Christian Andersen Diploma of Honour at the IBBY 25th Congress. She has illustrated (on her own and together with Steponavičius) 14 books. In 2010, she held her first personal exhibition at the Lithuanian National Gallery.