Olympian Lawrence won three of her six pool women’s individual epee matches before beating Romanian Amalia Tataran 15-10 in the last 32.
However, her European Games run was ended in the next round by Italy’s Giulia Rizzi, who claimed a 15-12 victory.
Lawrence, however, was reasonably happy with how she fenced, although she felt there were a couple of crucial points where she could have been technically better.
She said: “I fenced really well in the first few minutes, took my time quite a lot and committed to the actions, which is always the aim of the game when you’re fencing.
“She (Rizzi) changed a little and I was trying to keep up with her timings and distance but I couldn’t suss it out and she gained a couple of hits lead.
“I had to take more risks then and unfortunately for me those risks didn’t quite pay off today.
“It’s so hot, especially after eight minutes of fencing, but we are used to it and it’s all acclimatisation.
“Looking back I fenced really well today, there’s been a couple of points where technically I could have been a little bit better.
“But I’m pretty sharp and I’m looking forward to going to the World Championships in a few weeks and this is a good warm up for that.”