Working with printf in a bash script, adding no spaces after \"\\n\" does not create a newline, whereas adding a space creates a newline, e. g.: >
Your edited echo version is putting a literal backslash-n into the variable $NewLine which then gets interpreted by your echo -e. If you did this instead:
NewLine=$(echo -e "\n")
echo -e "Firstline${NewLine}Lastline"
your result would be the same as in case #1. To make that one work that way, you'd have to escape the backslash and put the whole thing in single quotes:
NewLine=$(printf '\\n')
echo -e "Firstline${NewLine}Lastline"
or double escape it:
NewLine=$(printf "\\\n")
Of course, you could just use printf directly or you can set your NewLine value like this:
printf "Firstline\nLastline\n"
or
NewLine=$'\n'
echo "Firstline${NewLine}Lastline" # no need for -e