You shouldn't be surprised if your SAS status is only applicable if that's the FF # on your boarding pass.
If you have non-status LH on your boarding pass don't be surprised if you're instructed to change your boarding pass FF # to SAS if you want to utilize the SAS benefits rather than non-status LH benefits. (YMMV)
I've never tried this with SAS and LH, but I've never run into this problem on other *A airlines.
I have transitioned from one *A program to another a few times now, and when doing so I show my existing *G card at check-in and for lounge access, while my boarding pass shows the non-status FFP.
This works for in-airport benefits (*G check-in, priority baggage tags (FWIW!), lounge access) but obviously not for benefits that are directly linked to the FF#/PNR (e.g. waitlist priority). Though I think I recall some threads discussing how some airlines allow you to enter two FF#s - one for miles earning and one for status. (I've never bothered with this.)