I don't think it's the math you are having a problem with - it's the concepts behind this. I will try and explain it as simply as I can without using too many numbers...
The most important point is that dBs aren't absolute units - you can set the reference point anywhere you like - as long as you've indicated where your reference value is. Pascals ( a microPascal is one millionth of a Pascal) are an absolute unit of pressure, so you can use these to indicate where you are setting your relative pressure reference value at. So for convenience with acoustic measurements, we can set our 0dB value to be at 20 micropascals, and that level is about where the threashold of hearing is - so everything louder than that has a positive number. And that's where things like the lawnmower get their values from. So strictly speaking, that should read 95dB ref 20 microPascals.
Audition of course has it the other way around - the reference you are worried about there is the point at which it overloads, and by custom and practice this has always been referred to as 0dB. So quieter sounds all have lower values than this. But the important thing is that this isn't an absolute pressure value - so doesn't relate directly to the real world of things making a noise at all. Which means of course that you cannot use Audition for these sorts of measurements - well, not directly anyway.
To measure real-world levels you have to use a Sound Pressure Level meter, and to be accurate, they have to be calibrated. This happens using a device producing a fixed-level tone at a known level. When you've calibrated your meter, then you can determine the levels of sounds using it. This is NOT simple and straightforward - I'm only giving you a brief overview of the situation; in practice there is a heck of a lot you have to understand and take account of before you can get a reliable value.
To a first approximation, using the 20 microPascal level as 0dB, then the threshold of hearing is at 0dB, and the threshold of pain is at about 120dB. When you are exposed for any length of time to sounds above about 85dB, you are likely to suffer from at least temporary hearing threshold shift - which is why it's set as the lowest 'action' level - for continuous exposure above it, you are advised to wear hearing protection. You are okay with the lawnmower for two reasons; firstly you aren't really exposed to it for that long as a rule, and secondly, the point at which 95dB is reached is at a fixed distance from the source of the noise, and you are actually further away than that - so it's not that loud at the place your ears are.