The 22-year-old won her first bout of the day against Chile’s Caterin Bravo Aranguiz, before losing 15-9 to Romania’s European champion and world number four Simona Gherman in the round of 32 in the individual epee.
But 2009 Commonwealth junior champion Lawrence believes she gave her best at the ExCel Arena and is looking forward to appearing at Rio in 2016 and beyond.
"This is a good platform on which to build for the next four to eight years – the 2016 and 2020 Olympics,” said Lawrence, who beat Aranguiz 15-12.
"I won one and lost one. It was a good fight. She is a great competitor.
“I put in my best and that’s all I can do – I put up quite a good fight so I’m pleased.
“I’m looking forward to enjoying the village more now.”
Lawrence, the only British athlete to be selected for the epee, feels she was given a huge lift by the passionate support of the home crowd.
She added: "It's brilliant. The crowd are really behind me, and it got me really psyched.
“I was a bit worried this morning as I didn't want to let anyone down but actually they're behind me whether I get a point or not.
“Obviously we’ve all been focusing on performance, and rightly so as that’s why we’re here but I can’t thank the supporters enough – having all the Brits in the crowd is absolutely tremendous.”