As Jobs became more successful with his new company, his relationship with Brennan grew more complex. In 1977, the success of Apple was now a part of their relationship, and Brennan, Daniel Kottke, and Jobs moved into a house near the Apple office in Cupertino. Brennan eventually took a position in the shipping department at Apple. Brennan's relationship with Jobs deteriorated as his position with Apple grew, and she began to consider ending the relationship. In October 1977, Brennan she realized she was pregnant, and that Jobs was the father. It took her a few days to tell Jobs, whose face, according to Brennan, "turned ugly" at the news. At the same time, according to Brennan, at the beginning of her third trimester, Jobs said to her: "I never wanted to ask that you get an abortion. I just didn't want to do that." He also refused to discuss the pregnancy with her. According to Brennan, Jobs "started to seed people with the notion that I slept around, and he was infertile, which meant that this could not be his child". A few weeks before she was due to give birth, Brennan was invited to deliver her baby at the All One Farm. She accepted the offer. When Jobs was 23 (the same age as his biological parents when they had him) Brennan gave birth to her baby, Lisa Brennan, on May 17, 1978. Jobs went there for the birth after he was contacted by Robert Friedland, their mutual friend and the farm owner. While distant, Jobs worked with her on a name for the baby, which they discussed while sitting in the fields on a blanket. Brennan suggested the name "Lisa" which Jobs also liked and notes that Jobs was very attached to the name "Lisa" while he "was also publicly denying paternity". She would discover later that during this time, Jobs was preparing to unveil a new kind of computer that he wanted to give a female name (his first choice was "Claire" after St. Clare). She stated that she never gave him permission to use the baby's name for a computer and he hid the plans from her. Jobs worked with his team to come up with the phrase, "Local Integrated Software Architecture" as an alternative explanation for the Apple Lisa. Decades later, however, Jobs admitted to his biographer Walter Isaacson that "obviously, it was named for my daughter".
When Jobs denied paternity, a DNA test established him as Lisa's father. It required him to pay Brennan $385 (equivalent to about $1,000 in 2021) monthly in addition to returning the welfare money she had received. Jobs paid her $500 (equivalent to about $1,400 in 2021) monthly at the time when Apple went public and made him a millionaire. Later, Brennan agreed to interview with Michael Moritz for Time magazine for its Time Person of the Year special, released on January 3, 1983, in which she discussed her relationship with Jobs. Rather than name Jobs the Person of the Year, the magazine named the generic personal computer the "Machine of the Year". In the issue, Jobs questioned the reliability of the paternity test, which stated that the "probability of paternity for Jobs, Steven... is 94.1%". He responded by arguing that "28% of the male population of the United States could be the father". Time also noted that "the baby girl and the machine on which Apple has placed so much hope for the future share the same name: Lisa".