If an NPC casts Secluded Grimoire, hiding his spellbook in the ethereal plane, and then dies, is the spellbook lost forever?

Secluded Grimoire states:

Duration instantaneous

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This spell sends a spellbook into a random but safe location on the Ethereal Plane, where it remains indefinitely. When you cast this spell, the target spellbook dissolves into quickly fading lines of energy and runes that reflect all of the spells stored within. Thereafter, you can retrieve the spellbook by concentrating as a standard action, causing it to reappear in your hands. You cannot cast this spell on another spellbook if you currently have a spellbook in the Ethereal Plane. No other creatures or objects accompany the spellbook you send away, and the duration of any spells currently affecting the spellbook continue normally.

The duration of instantaneous means that the spell will never wear off due to duration, therefore the only way to access it on the Material Plane is for the caster to spend a standard action to summon back into their hands. However the spellbook does actually exist in the Ethereal Plane, so a person with access to Plane Shift could go to the Ethereal Plane and get the spellbook.

However, since it's sent into a "random but safe location" the caster would have no idea where to look for it. This means they may not be able to find it, even with the help of a spell like Locate Object^[1], though that would require having seen the spellbook before (Wish could potentially be used to find it at the GM's discretion). This means that it'd be up to the GM whether you would be able to find it all while stumbling around on the Ethereal Plane.

^{[1]: Discern Location also works, but requires having actually touched the spellbook before, which is unlikely if you're not the caster who owns it.}

No

Regardless of the caster's life or death, an extraplanar expedition might be mounted to find it.

One also might instead make use of the Discern Location spell. With such magic, one might cast Plane Shift, then Greater Teleport, then Plane Shift, then Greater Teleport so as to fetch the object most succinctly.

If one were not trying to steal the spellbook but merely trying to retrieve it, it would certainly be simpler to merely raise the dead caster to life, then have them cast the spell to bring the book back, which would also work.

Beyond that, one might make use of myriad contingency plans the original caster may have made use of to make retrieval easier or more accessible to get the book, for example placing a ring gate near it or making use of either version of the Refuge spell. Many of these additional means of accessing the tome will have their own ways of exploitation or use.

Lastly, unlike leomund's secret chest (same link as above), secluded grimoire does not protect itself against Wish. Wish can move anyone anywhere else through any barriers with no chance of failure unless specifically warded against, so that would of course also work-- you could possibly go directly to the book and pick it up that way, too, depending on how the GM rules you can describe locations. If not, you could always try to use the open-ended abilities of the spell (or Miracle), but there are no reasons to do that.