With all due respect to the others, 2 things should be added.
1. While products like nut sauce do work, simply rubbing pencil lead on the bottom of the nut slot is endlessly cheaper and time tested.
and
2. In over 25 years, I have never seen
a properly cut nut need any form of lubricant to avoid going out of tune in any concievable real world scenario, including insane Floyd whammyage with locking tuners instead of a locking nut. If you´re getting tuning issues stemmuing from the nut, the cause is always either an improper cut or long term wear. Neither is IMO an excuse to sell someone a 10$ bottle of funkly fluid that will at best only mitigate the problem, but can never alleviate it.
I regard nut lubricants as a crutch for people who do not have easy access to a competent tech, and expensive ones as snake oil capitalizing on the ignorance of teh customer and the incompetence of most of the people that like to call themselves "techs".
In my professional opinion the only reason there is to pay anything at all for nut lubricants (especially more than a few cents in your lifetime for a simple pencil) is being swayed by flashy marketing and the parroting of other people that simply don´t understand the subject as well as they think they do.
The same holds true for roller bridges being "necessary" in Bigsby guitars according to some.. Again, total hogwash, just get your bridge saddles cut and deburred by a professional and save money in the long run
I don´t judge people for using nut sauce or similar products, they just want their guitar to stay in tune and every store in the world will gladly sell you some without telling you there are dirt cheap alternatives. But if someone "needs"it, that tells me they either don´t know or they can't afford /refuse to adequately pay a competent tech. And if they refuse to pay a competent tech but would rather use a crutch-product, they entirely deserve to waste money in this fashion. Everyone else just needs to try the pencil and /or find a tech worthy of the title.