Lum started corporate life as a chemist with Glaxo Pharmaceutical. After working for three years at Glaxo, she left in 1989 at the age of 28 to start up Hydrochem, the precursor to Hyflux, with just SG$20,000 of capital, which she raised by selling her condominium and car. She hired three employees at the start; Lum herself rode around on a motorcycle selling her company's water filters and treatment chemicals. By January 2001, Hyflux had become the first water treatment company to be listed on SESDAQ, and was upgraded to the Singapore Exchange's Mainboard in April 2003. By 2005, she had a net worth of over US$240 million, which earned her a place as the only woman on Forbes' "Southeast Asia Rich List". As of 2007, Hyflux was worth SG$1 billion and employed more than 800 people.
Lum holds several positions in public service. She is a board member of SPRING Singapore, the National University Singapore Council, and the Singapore Exchange, as well as the president of the Singapore Water Association. She is also a member of the UNESCAP Business Advisory Council and the Singapore Green Plan 2012 coordinating committee. Lum was a Nominated Member of Parliament in the Parliament of Singapore from 2 July 2002 to 1 January 2005. In 2003, she was awarded the International Management Action Award, followed by the Global Female Invent and Innovate Award the following year.
On October 3, 2008, Lum resigned her position as independent non-executive director of the Singapore Exchange and relinquished her position on the audit, regulatory conflicts and remuneration committees of the Exchange, according to the Exchange's filing. She stated this was due to her heavy work commitments in line with Hyflux's rapid expansion, and that her resignation would enable her to focus more time and resources on Hyflux's growth.