It looks like the list of LH lounges you found on the airport's website is somewhat out of date. Senator and Business lounges by gate A51 have been gone for a few years and replaced by the Tower Lounge near gate A65.
A more accurate information may be found on Lufthansa's website. Enter your status/class of travel and the airport on
this page and you will get a complete list.
You also need to bear in mind that some lounges are in Schengen and others are in non-Schengen and visiting them might involve going through passport control (and security).
In summary:
First Class Lounges/Terminal: FCT (landside outside main terminal), FCL A (Schengen above A26), FCL B (non-Schengen above B22)
Senator Lounges: by A26 (Schengen), central area B (non-Schengen), by C14/15 (non-Schengen)
Business Lounges: by A26 (Schengen), above B24-28 (non-Schengen), above B44-48 (non-Schengen), by C14/15 (non-Schengen), by C16 (non-Schengen), Tower Lounge (by A65 non-Schengen)
Arrivals Lounge: Welcome Lounge (landside near baggage claim B)
You can check departure gates of TK flights to IST on the
flight status page of lufthansa.com.
Yes, TK seems to use B gates but sometimes a bus gate on the lower level. For the last couple of days UA940 arrived at a B bus gate.