Are we talking about including video transcoding, or only audio, discarding video?
If including video, there may be an internal setting inside LAV Video thats badly tweaked for transcoding right now (already adjusted for the next version)
If no video, i don't see where it would Sleep.
The only place it ever sleeps is when the queues are overflowing in LAV Splitter, for example when you try to consume audio faster than video, it won't give you any more audio until you also used more of the video, to protect you from excessive memory usage from all the video that is waiting in memory.
However, if you just don't connect anything to the video pin, it'll be silently discarded and you should receive audio at I/O speed.