Given the complexity of LW2, by design, you'll probably have better luck using the https://www.greaterwrong.com/ mirror.
Yeah, the internet archive is doing some stuff that is a bit hard to work around with our architecture (it tries to execute our javascript bundle and then sends requests to nonexistent servers). It's been on my to-do list to fix for a while (probably by just somehow telling the archive to just serve the plain HTML versions of the pages that we send, or just making sure that our javascript bundle fails more gracefully when it gets called in the ways the internet archive is doing it).
Until then, backing up the greaterwrong mirror seems like something that gets us most of the value, though I do really want to get around to fixing the archive.org versions for the main site.
Related question on the EA Forum: https://forum.effectivealtruism.org/posts/vK4iAutzMSfamG5je/can-i-archive-the-ea-forum-on-the-wayback-machine
There are some great information on lesswrong.com (LW) that seems to be available publicly (I can access it in an incognito chrome window) and I would like to increase the chances of this information surviving for a long time.
When I try saving a LW page it looks like it does not render correctly on the wayback machine. Ex: https://web.archive.org/web/20200624170623/https://www.lesswrong.com/s/FrqfoG3LJeCZs96Ym/p/8qccXytpkEhEAkjjM
I opened a github issue on LW's repo since I assume it is an issue with the source code of LW. The EA forum seems to have the same issue and it looks like the EA forum's repo is a fork of lesswrong's repo. I am also writing here since it might have more visibility for non tech people.