Try to do it on LH. I did it in the past.
I logged into Lufthansa with my Swiss reservation code.
They required me to input my passport info, and the next page allowed me to request a special meal.
(My reservation has a few people. After inputting passport info for 1, I clicked the 'continue' on the bottom after the passenger list and was able to request meals for out whole group.)
Thank you.
(FYI: I got my Swiss reservation code when I logged into United using the reservation code they gave me when I booked the flight with them.
On the Swiss Air website I booked my seats.
On Lufthansa I ordered my kosher meal.)