rabbiofberlin – I believe that the shulchan aruch is speaking about women actually making the tzitzis – i.e. weaving the thread and material. It says that is ok
However, the remah says that it’s preferable for women not to tie tzitzis.
About the lulav – I must have been remembering incorrectly. women are allowed to tie the knots, but they are advised not to bind the hadassim and aravos to the lulav. This is in sync with what rabbiofberlin said about the knots not having to do anything with the mitzvah.