Originally Posted by Stuttgart21

Is the onward flight in Business Class as well? If so, you could access the Austrian lounges using your departing boarding passes to INN.

Otherwise, I would just go straight to the Sky Lounge Schengen and try it. They might not look at your onward boarding pass in detail. And if they do and tell you something about "three-hour maximum stay" or something I would just tell them the truth. You merely want to grab a quick coffee and a snack, freshen up, or whatever.

Originally Posted by MichaelA380

As the poster above has said, you will have to try your luck ... in order to have a chance of accessing the OS*A Business Lounge, your will either have to fly business to INN or hold at least M&M FTL status.

Your OS flight from AMS may arrive both at a remote stand or dock at a gate.
* If you arrive at a remote stand, the bus will take you to Schengen arrivals on the ground floor of Terminal 3. Once you enter the building, do not take the exit to Vienna but take the escalator up, which will take you up to Departures (this is the same floor on which the gate for your INN flight will be - as you are arriving from a Schengen origin and transferring to a domestic destination, you will not have to go through security).
* If you dock at a gate, once you reach the terminal, there will be signs. In can be that both signs point to the escalator up for exit and transfers, take the escalator, on the upper floor go to the end of the corridor and then take the escalator down to Departures. For some gates, there will be a sign up for exit to Vienna and a sign straight ahead for transfers - go straight ahead and you find yourself at Departures.
* In all cases, you will have to completely backtrack to the beginning of Departures, beyond Gate F1, then back through the food court and duty free to the exit from security - there you take a turn right and the escalator / stairs one floor up (look at the signs, everything is self-explanatory). Once there, follow the signs to the lounge area - once there you will see both lounges, OS*A on the right, Sky Lounge on the left. Feel free to try your luck whichever way you think you have better chances.

For getting out, exit the lounge, follow the signs to Gates F (which will require going a level down) and once at Departures take the nearest exit to Vienna sign.

By the way, all of the above assumes your luggage will be checked through to INN at AMS - otherwise, you will have to collect it at VIE, at check-in level there is a left luggage facility where you can store it and if at that point you still want to try your chances with the lounge, you will have to enter the secure area with your onward BP and go through security before following the process just described above.