To briefly set the scene, there are Global Top Level Domains (gTLD) such as .com, .net, .org, .info, etc. And Country-Code Top Level Domains (ccTLD) such as .us, .de, .uk, .pr, .to, .ly, etc.
When you register a domain name, you typically do so through a "Registrar," which is a licensed entity that is able to interact with ICANN ("The Internet Corporation for Assigned Names and Numbers"). For most domain extensions, you can do so through a well-known registrar such as Uniregistry, Moniker, Namecheap, etc.
However, some ccTLDs set their own rules and have their own registrar relationships. That seems to be the root of your question — is it worth registering a .ly domain given the potential uncertainty about their rules, safety, anonymity features, price, etc.
I really think that's a personal decision. You certainly can register it if you'd like — it appears that they welcome registrations by foreigners (so long as you follow some rules re: adult content). Some ccTLDs are strictly for local registration. And there are bigger companies that are using .ly domains: bit.ly being the most prominent off the top of my head.
But there might be some downsides and headaches:
If you're willing to put up with the headaches and slight uncertainty above, go for it. But for a personal project, it might be a bit more of a hassle (and a bit more expensive) than would be optimal.
Hope that helps!
 - FWIW, to my knowledge, the rules surrounding "accurate contact information" are very rarely enforced. The most important aspect of the registration to get right would be ensuring that you control the admin email on file.
Well, I just learned a whole lot.
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