Here is one approach to adding colored boxes to a box plot.
#Invent data
DF <- data.frame(LCZ = rep(1:3, each = 30),
Value = c(rnorm(30), rnorm(30, 1, 1), rnorm(30,4, 1)))
DF_Expect <- data.frame(LCZ = 1:3, Value = c(0.3, 1.2, 3.3), Height = c(1.3, 0.8, 1.7))
library(ggplot2)
#> Warning: package 'ggplot2' was built under R version 4.0.5
ggplot(DF, aes(LCZ, Value, group = LCZ)) + geom_boxplot() +
geom_tile(aes(x = LCZ, y = Value, height = Height, width = 0.7),
fill = "green", alpha = 0.5, data = DF_Expect)

Created on 2021-07-16 by the reprex package (v0.3.0)