Arguably, comprehend languages and tongues
The Ring confers immunity to magic that "allows other creatures ... to determine whether you are lying. Not, you'll notice, magic that determines whether you are lying, but magic that would allow another creature to reach such a conclusion.
So if I don't speak your language, and you use a spell to understand my speech, and I'm obviously lying to you (say I'm a bad liar and contradict myself), the magic is allowing you to determine that I'm lying, because otherwise you don't know what I'm saying. Therefore I'm immune to the magic and you can't comprehend my speech while I have the Ring on.
Note that the immunity has to apply even when I'm not lying, or else the spell would still enable you to determine that I'm lying by the fact that your translation stops working.
Arguably, any kind of scrying magic
"Prof. Moody": Good morning class! I'm Professor Moody! Constant vigilance! Today we're going to learn summon greater demon for legitimate educational reasons.
Hermione: Locate creature Professor Moody!
If the imposter is wearing a Ring of Mind Shielding, the magic should be unable to confirm or deny his claim to be Professor Moody, since this would allow Hermione to determine that he's lying. In fact no scrying magic can provide corroboration for any true or false statement of fact he's ever made. Or might make in the future. He emits a light cone of magical inscrutability in both directions.
And now things go off the rails
Alice: Hey, is that a Ring of Mind Shielding?
Alice: casts identify
If identify works, then it will confirm that Bob is lying. If identify doesn't work, then it also reveals that Bob is lying.
Possible solutions to the paradox are:
- Lots of other magic items resist being identified, so this by itself is not strong evidence that it's a Ring of Mind Shielding.
- Divination magic is generally unable to determine if something is a Ring of Mind Shielding. No actual Rings need to be present for this to happen. The abstract category of Rings of Mind Shielding resists magic.
- Identify will work just fine, but Alice will be weirdly unable to conclude that Bob is or isn't lying. Maybe she'll forget what he said, or assume he didn't know what the ring did, or just never be able to put the two facts together.
- The Ring will prevent Bob from answering the question in the first place, so that he can neither lie nor tell the truth about it.
- Or this whole line of reasoning is wrong and this particular magic immunity conferred by the Ring only protects against actual lie-detecting magic, if there is any, which there isn't in any published source as of yet. (Except for detect thoughts, which is already blocked by the Ring's other effects.)
I think the last of these is probably the intended function of the item, but it's the least fun option.