Hey there, @Nyxi!
Ryder here, from the Social Care Team at Shopify. Thanks for posting! I've done my fair searching of lanyard through quite a few of the Print on Demand apps in Shopify's App Store and had a hard time finding some too. That being said, I can recommend a couple other options for you that may be potential solutions for your business needs.
Through a quick Google Search, I was able to locate an online store called Imprint.com that supplies custom lanyards. While they do sell them individually, the prices are rather high so if purchasing them in bulk is feasible for you it may be worth considering. Another site I found is Custom Ink which looks like it gives you the price estimate after designing the lanyard. Of course, you can Google and browse through other external businesses to compare prices and shipping to see which one might be best for you. There are external suppliers which have private apps that can integrate with your Shopify store , so it never hurts to reach out and ask if that's something they offer!
Alternatively, if you use the Oberlo app, I know that AliExpress also has some suppliers that offer custom lanyards. You can browse through the listings here. Some suppliers require you to purchase in a minimum amount in each order - again, if wholesale is an option for your business then this is an avenue you can explore.
Whichever supplier you choose to source your lanyards from, it's a good idea to read reviews and even reach out to them directly to get an idea of the degree of customer service they provide. It'll help in the long run to know you can trust the supplier to respond if you're having an issue with an order. You can read more about finding and working with suppliers in Chapter 3 of our Dropshipping Guide.
I hope this information helps! If there's anything I can clarify, please let me know.