if the fast track in the main hall takes longer than the smaller one at K, wouldn't you be able to continue using the K security?
The BP scanner might still work I suppose, unless extra IT effort goes into it, as right now it obviously beeps green for all LH group BPs and TAP IIRC.
Bear in mind that if you proceed to the Star Alliance Lounge after security you have to take that extra walk anyway which means the time saved with shorter walk from HEX to checkin area is lost again with longer walk to the lounge. And most LH flights depart from the right wing of T2, so you need to walk in that direction anyway.