You need to return a value in your lapply
call:
mylist <- lapply(mylist,FUN=function(x) {names(x) <-
c("A","B","C","D","E","F","G","H","I","J",
"K","L","M","N","O","P","Q","R","S","T")
x ## <- note the x here; you could also use return(x)
})
mylist
# $One
# A B C D E F G H I J K L M N O P Q R S T
# "A" "B" "C" "D" "E" "F" "G" "H" "I" "J" "K" "L" "M" "N" "O" "P" "Q" "R" "S" "T"
#
# $Two
# A B C D E F G H I J K L M N O P Q R S T
# "A" "B" "C" "D" "E" "F" "G" "H" "I" "J" "K" "L" "M" "N" "O" "P" "Q" "R" "S" "T"
#
# $Three
# A B C D E F G H I J K L M N O P Q R S T
# "A" "B" "C" "D" "E" "F" "G" "H" "I" "J" "K" "L" "M" "N" "O" "P" "Q" "R" "S" "T"
#
# $Four
# A B C D E F G H I J K L M N O P Q R S T
# "A" "B" "C" "D" "E" "F" "G" "H" "I" "J" "K" "L" "M" "N" "O" "P" "Q" "R" "S" "T"