$ perl -pe 'BEGIN{ chomp(@a=`cat file2.txt`) } s/^!!.*/$a[$i++]/e' file1.txt 
aaaaaa
bbbbbb
first line
second line
ccccc
ddddd
third line

• @a array stores all the lines from file2.txt with ending newline character chopped off. BEGIN block to execute this line of code once at start of script
• s/^!!.*/$a[$i++]/e substitute lines starting with !! with value from @a array. Index is saved in $i variable (default value zero) and gets incremented for every access. The e flag enables use of code instead of string in replacement section

With GNU sed, similar to awk+getline

$ sed -e '/^!!/{R file2.txt' -e 'd}' file1.txt
aaaaaa
bbbbbb
first line
second line
ccccc
ddddd
third line

• R would give a line one at a time
• order is important, first R and then d

$ < file2.txt perl -pe '$_ = <STDIN> if /^!!/' file1.txt
aaaaaa
bbbbbb
first line
second line
ccccc
ddddd
third line

• pass the file with replacing lines as standard input, so that we can read it using <STDIN> filehandle
• if matching line is found, replace $_ with a line from standard input