Was also stuck with problem of LS for output contol in outbound delivery. ERP -> PI scenario. The solution is VERY weird and unlogical.
Just use 'SH' instead of 'LS' in condition control in NACE.
Then the delivery output will look like this:
In WE02 we see that IDOC was sent to right destination:
Also be sure that WE20 Partner profile is configured for LS and you have correct distibution model in BD64, and the medium MUST be ALE.
BD64:
Hope it helps.