While I haven't heard the BHSE, (yet, but I'm working on it, har, har) I can say that with a balanced source my LL/009 was always at around 11 o'clock for a comfortable listen. Even 1 PM was waaay too loud for these ears.
I'm giving myself a break from headphone listening for the rest of the summer, then come winter I'll probably get another 009 and either borrow or buy both the LL and BHSE so I can figure this out for myself. I've exchanged way too many PMs with other LL owners who for some reason or other seem reluctant to publicly post just how good the LL is, but have no qualms stating so privately. Am I missing something here?
Headfier IanG visited my place yesterday evening along with his LL + SR-007mk1's to which we listened to both his 007's and my 009's driven by his LL + my BHSE. When first hearing the LL I have to say I'm quite impressed with how it made both headphones sound, but the 009's sounded better of the two. I felt the same about the BHSE, the 009's were more detailed and transparent than the 007's but like some headfiers have said volume is an issue with the 009's driven by the BHSE. About volume, when using the 009's with the BHSE my optimum level is between 11 and 12 o'clock but with the 007's I could easily go beyond 2 o'clock. The LL is a different matter, with the 009's it's around 3 o'clock but 007's is between 4 and 5 o'clock to get the same volume the BHSE gives at 2 o'clock. Build quality, I went for the $6000 version of the BHSE and it was worth that on build quality alone, I've no comment about the LL's build quality other than the fact that it's headphone sockets are extremely tight, when I tried to unplug my 009's from it I was afraid the pins were going to stay in it's socket. If it was only down to sound quality, I would have strongly considered buying the LL if I didn't have the BHSE, but other things about it would deter me.
P.S. The 009's when at the right volume with the BHSE, meaning not too loud, for me give the best SQ I've ever heard.