Many know and love Lim for his role as patriarch Tan Ah Teck in Singapore's first and one of its most popular sitcoms Under One Roof which ran from 1995-2003. The show was the first successful English show by Mediacorp's Channel 5 that was sold internationally. It also starred Koh Chieng Mun, Vernetta Lopez, Andrew Lim and Nicholas Lee. 

In 1996 and 1997, Under One Roof won the Best Comedy or Series Award at the Asian Television Awards. The show was also a finalist in the Best Sitcom category at the International Emmy Awards as well as the New York Festivals Awards. 

The success of Under One Roof paved the way for future local sitcoms like Phua Chu Kang Pte Ltd, Mr Kiasu and Police & Thief. 

Lim’s portrayal of Tan Ah Teck also led him to become the first Singaporean to win the Asian Television Awards for Best Male Actor in a Comedy (Comedian) in 1996.

In the show, Lim’s character Tan Ah Teck is often prompted by any situation to tell his stories with the intention to teach the other characters some moral lesson and to impart nuggets of wisdom.

The stories frequently begin with his famous catchphrase "This reminds me of a story! Long before your time, in the Southern province of China...". Many still remember his iconic line till this day. 

In 2004, Lim received the Top 10 Most Popular Male Artistes Award during Mediacorp’s Star Awards.

Thereafter, Moses Lim focused more on films and other productions. In 2007, he played director Eric Tan in Just Follow Law directed by Jack Neo and in 2012, he performed in the stage play, Happily Ever Laughter. In 2015, Lim also starred in Our Sister Mambo, a film to mark Cathay Organisation's 80th anniversary.