Yes, with its recovery link (saved, or emailed to your backup address), or by signing in on the browser you made it in; without either, you can't edit it again.
Edit access stays in the browser you made the list in, so clearing that browser's data or switching devices leaves it behind. "Do I need an account?" explains what that browser keeps.
Steps
Find your recovery link: the one you saved, or the email "Your backup link for" plus your list's name.
Open it in Safari or Chrome. If it opens inside Instagram, Telegram or your mail app, use that app's ⋯ menu to open it in your browser, or paste the link into Safari or Chrome.
Tap Claim ownership. If you're signed in, the list joins your account. If not ("Restore access to this wishlist"), this browser becomes its owner. The old browser loses edit access either way.
No recovery link, but you still have the browser? Move the list into an account from there instead: "Do I need an account?" has the steps.
How do I protect a list before I lose it?
Open the list in the browser you made it in and tap the Protect access shield in the bottom-left corner (it shows up once the list has wishes). "Protect your edit access" gives you a choice:
Tap Add a backup email, type an address and tap Send backup link. Keep that email.
Or tap Get a recovery link, then Copy next to the link (an icon on a phone), and save it somewhere safe.
Or tap Sign in, and the list moves into your account.
Seeing "Too many attempts."? Wait a few minutes and try again. On Home, Protect next to "Protect your list" is a shortcut to the last option: it goes straight to sign in.
Seeing "Email already in use"? That address already has an account, so sign in with it on this browser instead.
Signing up later with your backup address doesn't bring the list back by itself, so open the link in that email.
Why doesn't my recovery link work?
"This link is invalid or has already been used." means the list was deleted, it's already in an account (claimed with this link, or you signed in on the browser you made it in), or the link got cut off when you copied it. If it went into your account, sign in and it's in your lists.
"The recovery link is missing or broken." means part of it got lost too, so copy the whole link again.
Reserved a gift without an account? See "Where can I see the gifts I've reserved?".
Tips
Have an account, or happy to make one? Sign in first, then open the recovery link, so the list goes straight into your account and isn't tied to one browser again.
Save the recovery link in your notes or password manager, not in a chat.
Treat it like a key: anyone who opens it can take over editing, so don't send it with the list's link.