Before overleaf, most people installed Latex locally (see e.g. texlive on Linux, miktex on Windows, etc), and then used their editor of choice (dozen of options here, ranging from dedicated Latex IDE like textudio, texmaker, etc. to more general editors like emacs, etc). LyX is nice too, essentially it's just a particular IDE (i.e. a nice way to edit a latex file without looking directly at the source file). To collaborate (or just backup), they used a cloud provider (e.g. Dropbox is pretty popular in academia); these days, some ppl use private github repo to work collectively on a paper (but you can do that even if you are the only one editing the file, of course).

Would one of these options that work for you? or do you specifically need something that does not rely on a local installation?