Bartoli, the French ninth seed, lost 6-4 6-3 to the Croatian, who was beaten by Steffi Graf in the ’99 semi-finals and then beset by problems off the court which interrupted and almost ended her career.
Lucic, 30, will face Italy’s Roberta Vinci in her next match.
Vinci booked her place in the last 32 with a 6-4 6-3 win over Marina Erakovic while Tamira Paszek, who upset seventh seed Caroline Wozniacki in round one, brushed aside Alize Cornet 6-2 6-1.
With the exception of Bartoli, it was a good day for the remaining seeds.
Defending champion Petra Kvitova took another step towards retaining her title while Maria Sharapova, Serena Williams and Victoria Azarenka also all progressed.
Top seed Sharapova resumed against Bulgarian Tsvetana Pironkova in a match which had been suspended due to bad light on Wednesday night.
Sharapova was one set and a break ahead overnight but lost the second set on a tie-break. However, the 25-year-old Russian hit back in the third set to win 7-6 (7/3) 6-7 (7/3) 6-0 and will next play Chinese Taipei’s Su-Wei Hsieh.
After the match, Sharapova insisted her grunt is here to stay following the WTA’s decision to drive excessive noise out of the game in the next generation of players. That means Sharapova will not be ordered to tone down her grunting, which is among the loudest on tour, and even if such a request came she doubts she could comply.
“Certainly not now,” she said, “not since I’ve been doing it since I was four years old. It’s definitely tough and impossible to do when you’ve played this sport for over 20 years.”
Second seed Azarenka made light work of her match against Romina Oprandi, winning 6-2 6-0, while Kvitova ended Briton Elena Baltacha’s hopes of progressing to the third round with a 6-0 6-4 win.
Baltacha failed to put up any fight in the first set against the fourth seed but raised her game towards the end of the second, however she always had a mountain to climb with Kvitova always looking to be too strong.
Serena Williams, who is seeking her fifth women’s singles title, brushed aside Melinda Czink 6-1 6-4.
The sixth seed will face China’s Jie Zheng in the fourth round after the 25th seed won her match against Canada’s Aleksandra Wozniak.
German eighth seed Angelique Kerber recovered from a break down in the opening set to topple Russian Ekaterina Makarova 7-5 6-3.
Francesca Schiavone also came through her second-round match, beating Kristyna Pliskova 6-4 6-4.
Ana Ivanovic progressed into the third round after she beat Kateryna Bondarenko 6-3 7-6 (7/3).
The No 14 seed will face Germany’s 22nd seed Julia Goerges who triumphed 7-6 (7/3) 6-2 against Anastasiya Yakimova.