"Must" may be too strong, this is LHG. One would assume this is or should the case, but when cost-cutting and LH come into play, anything is possible.

Had a horrible experience yesterday: whenever +1 travels with me, we use the security fast track together, although she is now only Frequent Traveller (*S); never had an issue when travelling with me. Yesterday, we were refused to use the Gold Track (as we had done at many airports before) and they sent her back to regular security. When I asked why they told us that LH has stopped paying for companions of SENs using the Gold Track. Apparently the benefit depends on the airline and, to my surprise, LH has decided not to pay, while some other *A carriers still do. So I can take her with me into the lounge and she also gets the same boarding group (as this doesn't cost LH anything), but she cannot use fast track security with me at some airports, which essentially means I also cannot use it when traveling with her (for obvious reasons).