Hello Jessica98
I have been going through the procurement for this lens cap. Order from:
https://www.also.ch/ec...
01 Enter the article number - you will find it in the quick start guide.
02 Order at https://www.also.ch
03 Delivery only against payment in advance: Cover approx. CHF 18.00 + postage CHF 14.00
04 Delivery approx. 3 weeks after payment

Conclusion: Elaborate, expensive, but it works.

This also happened to me.
The lens cap has the Panasonic part number: 1ZE1DCFZ1000M2Z

Unfortunately not available anywhere. I have already made several attempts. Panasonic offers the Panasonic DMW-LFAC1 lens cap as a camera accessory for the DC-FZ1000 II. However, it only works when no filter is mounted.
The information on this product is not very conclusive, so I will not buy it because it may not fit the camera after all.
https://www.panasonic.com/de...
Panasonic DMW-LFAC1
Maybe Panasonic support can help.

Jessica, you're way off. It's 62 mm, which is stamped on the lens cap of my camera as well as on the matching polarising filter. To be sure, I have the FZ1000 II as you specified.