The InfluxDB experience is definitely illuminating. Their problems with LMDB were mainly due to misuse of the API. https://disqus.com/home/discussion/influxdb/benchmarking_lev...
For batched sequential writes, there is no other DB anywhere near as fast as LMDB http://symas.com/mdb/microbench/ (Section E, Batched Writes)
But even so - the reason LMDB can do this so quickly is because for batched sequential writes it cheats - it's just performing Appends, there's no complicated tree construction/balancing/splitting of any kind going on.
If you know that your workload will only be producer/consumer, with sequentially generated data that is sequentially consumed, it's a stupid waste of time to mess with any other structure than a pure linear queue. (Or a circular queue, when you know the upper bounds of how much data is outstanding.)
As for your initial statement - no, an LSM tree is not a correct pattern here. If your consumers are actually running as fast (or faster) than your producer then it should never flush from Level0/memory to Level1/disk. In that case all you've got is an in-memory queue that evaporates on a system crash.
If your consumers are running slower, that means data is accumulating in the DB, which means you will have compaction delays. And the compaction delays will only get slower over time, as more and more levels need to be merged. (Remember that merge operations are O(N). Then remember that there are N of them to do. O(N^2) is a horrible algorithmic complexity.) LSM is never a correct pattern.