I want to be clear, I am not asking how long a lure last (30 min). I'm asking; starting from the time that a Pokemon spawns from a lure how much time do I have to catch it before it disappears? Is it a set amount of time? Does it vary and if so what seems to be the average amount of time?
Lures last for 30 minutes.
From there, approximately six Pokemon will spawn on a Lure through its lifetime. Therefore, a Lured Pokemon will typically stay available for around five minutes.
Note that this is affected by Pokemon rarity and other random factors, very much in the same way Incense spawns Pokemon.
The consensus in this question is that Pokemon are generally around for 15 minutes. This seems reasonable for a lure as well, as they spawn every five minutes, and I usually see two-three Pokemon at a spot that has had a lure on it for a while.