SQLite has the problem of a malicious reader being able to hold up writers. Maybe that's fine in most cases, but in a system log, I don't think that's acceptable. IMHO, options are to indirect through a daemon anyway (e.g. using Quack) or do a lot of engineering to make it possible for an unprivileged reader to open() the log file and read it in such a way that it can't interfere with privileged writers.
Your LSM compaction strategy is going to have to solve the same problem anyway, isn't it? DuckDB is an LSM compaction strategy of this form, already done.