On the first day, Lucca ate 1/4*200 = <<1/4*200=50>>50 pieces.
The number of pieces remaining after the first day is 200-50 = <<200-50=150>>150
On the second day, Lucca ate 2/5*150 = <<2/5*150=60>>60 pieces of bread.
The pieces of bread that remained after the second day is 150-60 = <<150-60=90>>90
If Lucca ate half of the remaining pieces of bread on the third day, he ate 1/2*90 = 45 pieces.
The pieces of bread that are remaining after the third day are 90-45=<<90-45=45>>45.
#### 45