'Поиск' должен быть построен в обратном порядке, т.е. имена должны совпадать со значениями в 'Графике'
library(dplyr)
lookup1 <- with(stack(lookup), setNames(as.character(ind), values))
ApMay %>%
mutate(Plot=lookup1[Plot])
# Plot CanopyHeight Date Time date
#1 WH104C1 1712.169 4/25/2019 4 2019-04-25
#2 WH104C1 1712.169 4/25/2019 4 2019-04-25
#3 WH104C1 1728.224 4/25/2019 4 2019-04-25
#4 WH104C1 1728.411 4/25/2019 4 2019-04-25
#5 WH104C1 1681.975 4/25/2019 4 2019-04-25
#6 WH104C1 1691.742 4/25/2019 4 2019-04-25
data
ApMay <- structure(list(Plot = c("WH102A2", "WH102A2", "WH102A2", "WH102A2",
"WH102A2", "WH102A2"), CanopyHeight = c(1712.169, 1712.169, 1728.224,
1728.411, 1681.975, 1691.742), Date = c("4/25/2019", "4/25/2019",
"4/25/2019", "4/25/2019", "4/25/2019", "4/25/2019"), Time = c(4L,
4L, 4L, 4L, 4L, 4L), date = c("2019-04-25", "2019-04-25", "2019-04-25",
"2019-04-25", "2019-04-25", "2019-04-25")), class = "data.frame", row.names = c(NA,
-6L))