I presume you are following this guide https://wiki.lyx.org/LyX/InstantPreview
The Preview package is related to preview-latex as used by auctex BUT is effectively a generic subset it is the standard preview package that should be loaded using TeX Live ManaGeR I do not know Unix well enough to advise with confidence but if you used sudo for texlive would guess you need something along the lines of
sudo tlmgr install preview however I suggest you test with
sudo tlmgr install --dryrun preview per the following guide to check it will work https://www.tug.org/texlive/doc/tlmgr.html#install-option...-pkg
If you have a GUI access to tlmgr (which requires the perl components) you can filter a package search to see if it is already installed. see https://www.tug.org/texlive/doc/tlmgr.html#GUI-FOR-TLMGR
Once it is downloaded you will need to consider if you need to run
sudo texhash to update filename/directory database files
If you cannot use tlmgr then the uncompiled file is available here and will need to be run through TeX http://mirrors.ctan.org/macros/latex/contrib/preview.zip
To install the preview style file on its own without the entire AUCTeX
If preview.ins happens to be missing, you can regenerate it by running
tex docstrip on preview.dtx with the option `installer'.
Running TeX on preview.ins will then extract further files: preview.drv which you can run through LaTeX in order to get the
documentation for preview.sty, preview.sty itself, a bunch of option
files with extension .def and a few configuration files with extension
.cfg. In case your docstrip configuration has not already taken care
of that, install the files with extension .sty, .def and .cfg to a
location where LaTeX will be able to find them.
The location as mentioned can be either your working folder alongside the tex file you are editing or in the correct relative location on a texmf tree.
Thus wherever your …/texmf is in the texmf/tex/latex you need a /preview/ folder with the preview.sty 8x filename.def (especially the LyX one) and the prauctex.cfg (though in this LyX case unsure if that's essential)If it is in the correct position lyx will find it and in Help > Latex configuration > in my version it is 9.27 preview it should show Found: [yes]
Note in my manual it is not the correct path for the switch in my version its in Tools > Look & Feel Display then tick Display graphics & ensure Instant preview On note you can also add scaling like this
Your quality may differ depending on settings and packages for support from the "Additional" help page the default formats can result in rougher image rendering. Document settings > Formats > defaults to PDF (pdfLaTeX) and generally does not need the external shell escape active but your mileage may vary, the XHTML Options are by default set strict XHTML and math output should be MathML but from the help we see section 4.1 that if those are unsupported by the system it will default to image rendering Quality is also affected as per user guide section 6.12.1 Prerequisites Results should be better if pnmcrop is available from netpbm package.