Lim‘s interest in comics began as a child, when he read comics and drew his favorite heroes, including Batman and the Fantastic Four.
His first published work was for the independent comic book title Ex-Mutants, which he worked on from 1986 to 1988.
He was “discovered” by Marvel at a 1987 comic convention, and was hired on the spot. Lim penciled the Silver Surfer(vol. 3) series for almost six years (1988–94). He also penciled most of the “Infinity” trilogy of large-scale crossover limited series which Marvel published in the early 1990s—Infinity Gauntlet (1991), Infinity War (1992), and Infinity Crusade(1993). He returned to these characters to pencil the Thanos series in 2004.
He was also a regular artist on Captain America in 1990–1991, while he was also working regularly on Silver Surfer. Other Marvel series he worked on during the 1990s include X-Men 2099 (1993), Spider-Man Unlimited, Dragon Lines (1993), and Venom: Lethal Protector (1993).
While Lim primarily worked at Marvel, he also worked at DC for a time in the late 1990s, providing art for the third and final year of Chris Claremont’s Sovereign Sevenseries. He also provided cover art & fill-in interiors for series like Hawkman, Green Lantern (vol.3) and Flash (vol. 2).
He has done work for the Sonic the Hedgehog franchise at Archie Comics, including Sonic #100.
In 1999 he was attached as artist to a failed revival of G.I. Joe to be published by Bench Press Comics with Larry Hama attached as writer.
Lim was a founding contributor to the ill-fated publisher Future Comics, and in 2002 penciled their fourth series, Metallix, for six issues.
Lim returned to Marvel in the 2000s illustrating several series associated with Marvel & Tom DeFalco’s MC2 imprint, including Avengers Next, J2 and the Fantastic Five. He contributed art in 2007 to the comic adaptation of Laurell K. Hamilton’s Guilty Pleasures, and since 2016 has been regularly providing variant covers for various Marvel one-shots, mini-series and event comics.