The defending champion sprayed court Philippe Chatrier with unforced errors in a match that was not as one-sided as the scoreline suggested.
Williams was so confident she would crush her training partner that she warmed up for the encounter wearing a blazer suit, but Lim proved to be a tenacious opponent despite her ranking of 138.
In the opening set, Lim claimed 27 points but surprisingly 23 of those came thanks to Williams's unforced errors.
Williams wasted four match points in the second set before wrapping it up on the fifth when her opponent sent a backhand long.
Williams, who could face her older sister Venus in the third round, did not want to put too much pressure on her shoulders, having already won the tournament twice.
"This year I'm just going day by day. I do have to say this year I don't feel as much pressure on myself as I did last year," she told a news conference.
"And that's it. I just am doing the best I can."
Lim never seemed to believe that she could be the second player to beat Williams in the first round of a grand slam.
Asked if she was scared to play against Williams, with whom she sometimes trains at the Mouratoglou tennis academy, Lim said: "Just after the draw, because very often that's the kind of match she plays against other girls.
"So I tried to focus having positive thoughts, and I thought to myself, Okay, I have played boys and it can't be worse.
"She doesn't come from another planet, so if I can move well and I can hit my ball well, there is no reason she should win 6-0 6-0."
Polish third seed Agnieszka Radwanska capitalised on Chinese Zhang Shuai's meltdown to advance.
As clouds rapidly gathered over Court Philippe Chatrier on a chilly morning, the first seven games went against serve before Radwanska bagged the remaining eight games.
She ended her hapless opponent's ordeal on the first match point with a fine volley to set up a meeting with Karolina Pliskova of the Czech Republic or French wildcard Mathilde Johansson.
"It's important that I settled in two sets and spent only one hour on court," Radwanska told a courtside interviewer.
Venus Williams, wearing a self-designed dress that added splashes of colour to a grey day, showed she is still a force at the age of 33 by taking, and returning, all that Belinda Bencic could throw at her in winning 6-4 6-1.
The 17-year-old Bencic, coached by Martina Hingis's mother, traded low, hard blows with the American from the back of the court but Williams had too much experience for the Swiss.
Another Chinese, Zheng Jie, was also among the early losers, going down 6-7(2) 6-3 6-4 to Anna Schmiedlova of Slovakia. Daniela Hantuchova, another Slovak and seeded 31, came from a set down to beat Jovana Jaksic of Serbia 2-6 6-2 6-4.
Results from the French Open Women's Singles Round 1 matches on Sunday
Varvara Lepchenko (U.S.) beat Petra Cetkovska (Czech Republic) 6-4 6-1
Tsvetana Pironkova (Bulgaria) beat Annika Beck (Germany) 6-7(5) 6-3 6-2
Johanna Larsson (Sweden) beat Maria Kirilenko (Russia) 6-1 6-2
8-Angelique Kerber (Germany) beat Katarzyna Piter (Poland) 6-3 6-1
Garbine Muguruza Blanco (Spain) beat Grace Min (U.S.) 7-5 7-6(6)
Yvonne Meusburger (Austria) beat Amandine Hesse (France) 3-6 6-3 6-4
Monica Niculescu (Romania) beat 25-Kaia Kanepi (Estonia) 5-7 6-3 6-1
Claire Feuerstein (France) beat Olga Govortsova (Belarus) 6-1 7-5
14-Carla Suarez Navarro (Spain) beat Yuliya Beygelzimer (Ukraine) 7-5 7-5
1-Serena Williams (U.S.) beat Alize Lim (France) 6-2 6-1
29-Venus Williams (U.S.) beat Belinda Bencic (Switzerland) 6-4 6-1
Anna Karolina Schmiedlova (Slovakia) beat Zheng Jie (China) 6-7(2) 6-3 6-4
31-Daniela Hantuchova (Slovakia) beat Jovana Jaksic (Serbia) 2-6 6-2 6-4
3-Agnieszka Radwanska (Poland) beat Zhang Shuai (China) 6-3 6-0
Follow the French Open on up to 7 courts LIVE on
- Sports & Recreation
- Agnieszka Radwanska
- Venus Williams