Conway grew up in White Plains, New York. Conway was shy and experienced gender dysphoria as a child. She became fascinated and engaged by astronomy (building a 6-inch (150 mm) reflector telescope one summer) and did well in math and science in high school. Conway entered MIT in 1955, earning high grades but ultimately leaving in despair after an attempted gender transition in 1957–58 failed due to the medical climate at the time. After working as an electronics technician for several years, Conway resumed education at Columbia University’s School of Engineering and Applied Science, earning B.S. and M.S.E.E. degrees in 1962 and 1963.

Conway was recruited by IBM Research in Yorktown Heights, New York in 1964, and was soon selected to join the architecture team designing an advanced supercomputer, working alongside John Cocke, Brian Randell, Herbert Schorr, Ed Sussenguth, Fran Allen and other IBM researchers on the Advanced Computing Systems (ACS) project, inventing multiple-issue out-of-order dynamic instruction scheduling while working there. The Computer History Museum has stated that “the ACS machines appears to have been the first superscalar design, a computer architectural paradigm widely exploited in modern high-performance microprocessors.”

Although she had hoped to be allowed to transition on the job, IBM fired Conway in 1968 after she revealed her intention to transition to a female gender role.

Upon completing her transition in 1968, Conway took a new name and identity, and restarted her career in what she called “stealth-mode” as a contract programmer at Computer Applications, Inc. She went on to work at Memorex during 1969–1972 as a digital system designer and computer architect.

Conway joined Xerox PARC in 1973, where she led the “LSI Systems” group under Bert Sutherland. When in PARC, Conway founded the “multiproject wafers” (MPW). This new technology made it possible to pack multiple circuit designs from various sources into one single chip. Her new invention increased production and decreased costs. Collaborating with Ivan Sutherland and Carver Mead of Caltech on VLSI design methodology, she co-authored Introduction to VLSI Systems, a groundbreaking work that would soon become a standard textbook in chip design, used in nearly 120 universities by 1983. With over 70,000 copies sold, and the new integration of her MPC79/MOSIS innovations, the Mead and Conway revolution became part of VLSI design.

In 1978, Conway served as visiting associate professor of electrical engineering and computer science at MIT, teaching a now famous VLSI design course based on a draft of the Mead–Conway text. The course validated the new design methods and textbook, and established the syllabus and instructor’s guidebook used in later courses worldwide.

Among Conway’s contributions were the invention of dimensionless, scalable design rules that greatly simplified chip design and design tools, and invention of a new form of internet-based infrastructure for rapid prototyping and short-run fabrication of large numbers of chip designs. The new infrastructure was institutionalized as the Metal Oxide Semiconductor Implementation Service (MOSIS) system in 1981. Two years into its success, Mead and Conway received Electronics Magazine’s annual award of achievement. Since then, MOSIS has fabricated more than 50,000 circuit designs for commercial firms, government agencies, and research and educational institutions around the world. VLSI researcher Charles Seitz commented that “MOSIS represented the first period since the pioneering work of Eckert and Mauchley on the ENIAC in the late 1940s that universities and small companies had access to state-of-the-art digital technology.”

The research methods used to develop the Mead–Conway VLSI design methodology and the MOSIS prototype are documented in a 1981 Xerox report and the Euromicro Journal. The impact of the Mead–Conway work is described in a number of historical overviews of computing. Conway and her colleagues have compiled an online archive of original papers that documents much of that work.

Conway joined the University of Michigan in 1985 as professor of electrical engineering and computer science, and associate dean of engineering. There she worked on “visual communications and control probing for basic system and user-interface concepts as applicable to hybridized internet/broadband-cable communications”. She retired from active teaching and research in 1998, as professor emerita at Michigan.

In 1987, Conway met her husband Charles “Charlie” Rogers, a professional engineer who shares her interest in the outdoors, including whitewater canoeing and motocross racing. They soon started living together, and bought a house with 24 acres (97,000 m) of meadow, marsh, and woodland in rural Michigan in 1994. On August 13, 2002, they were married. In 2014, the University of Michigan’s The Michigan Engineer alumni magazine documented the connections between Conway’s engineering explorations and the adventures in her personal life.

When nearing retirement, Conway learned that the story of her early work at IBM might soon be revealed through the investigations of Mark Smotherman that were being prepared for a 2001 publication. She began quietly coming out as a trans woman in 1999 to friends and colleagues about her past gender transition, using her personal website to tell the story in her own words. Her story was then more widely reported in 2000 in profiles in Scientific American and the Los Angeles Times.

Conway was a cast member in the first all-transgender performance of The Vagina Monologues in Los Angeles in 2004, and appeared in a LOGO-Channel documentary film about that event entitled Beautiful Daughters.

In 2009, Conway was named one of the “Stonewall 40 trans heroes” on the 40th anniversary of the Stonewall riots by the International Court System, one of the oldest and largest predominantly gay organizations in the world, and the National Gay and Lesbian Task Force.

In 2013, with support from many prominent thought-leaders in high-technology, Conway and her colleague Leandra Vicci of the University of North Carolina at Chapel Hill successfully lobbied the Board of Directors of the Institute of Electrical and Electronics Engineers (IEEE) for transgender inclusion in the IEEE’s Code of Ethics. That Code, known within the profession as much as a code of honor as one of ethics, became fully LGBT inclusive in January 2014, thus impacting the world’s largest engineering professional society, with 425,000 members in 160 countries. In 2014, Time Magazine named Lynn as one of “21 Transgender People Who Influenced American Culture.” In 2015 she was selected for inclusion in “The Trans100”.