This version of the software, that came with the Sony turntable - which was probably manufactured before 2016 as it has the old Sony software disc with it - is a limited edition of an old Sony product which is no longer supported by Sony.
If there is no serial no on the disc jacket or packaging then it is unlikely you will get a serial number for the software, if you do find serial number you may find it wants to register with Sony, however it will not because they no longer own the product.
Magix bought out a range of Sony products in 2016 and the current version is Sound Forge Audio Studio 13 is here , however you will have to buy it.
You could also try the free version of Music Maker for recording from the turntable.
Don't know anything about the Sony PS-LX300USB Turntable package, but normally with Sony Creative Software (SCS), the serial key would on the disc or the disc's envelope, I was not aware there even was an LE version of AS-9 . I do not think Magix can be of any help since AS-9 was a SCS product. I would contact Sony support for that particular product and the seller as well. It really sucks Sony would include software that can't be used, not to mention unethical and probably illegal.
You asked a very similar question in this earlier thread. Please do not start a new thread but simply continue to post in the older one. That way, responders can get a complete picture of the problem and what has already been suggested to you.