Anything, as long as 1) it's chosen, written, and formulated in a way that shows alignment with the values of the community, taken in a broad way; 2) doesn't make LW look bad to outsiders. (There have been cases of mods stepping in, or the community shutting down certain insistent debaters, when it came to certain discussion topics, for reasons of it being very bad PR.)
The first condition in fact could be generalizable to pretty much any human group (deviations from this norm might be taken to be, basically, trolling), and is more restrictive than it may look at a first sight. Just like in real life, apply common sense. Your message may not be technically flawed, but the success of your act of communication depends on the audience as well. People might wonder why you're telling that to them in particular. If you have lurked enough, you might already have a sense of what this community is about.
Sometimes users on LW try to establish a group discussion on topics that are not popular with most LWers, but they may be successful if people get the message that the OP values and desires the same things as them: intelligence, rationality, profound and insightful commentary, ethical behaviour and so on. Celebrity gossip, for instance, at an object level, probably cannot be adapted so that LWers receive it well, but a discussion on the role of celebrity gossip in people's lives and how it relates to populist/egalitarian status-regulating mechanisms targeted at undeservedly high status people -- that might fly.
For example, what would be inappropriately off topic to post to LessWrong discussion about?
I couldn't find an answer in the FAQ. (Perhaps it'd be worth adding one.) The closest I could find was this:
However "rationality" can be interpreted broadly enough that rational discussion of anything would count, and my experience reading LW is compatible with this interpretation being applied by posters. Indeed my experience seems to suggest that practically everything is on topic; political discussion of certain sorts is frowned upon, but not due to being off topic. People often post about things far removed from the topics of interest. And some of these topics are very broad: it seems that a lot of material about self-improvement is acceptable, for instance.