This is a slightly different question to "How close do you need to be to a poke-stop?"
I want to know if a lured Pokemon at a Pokestop only appear next to the stop if you are within the activation range of it? I sat outside of a Pokestop that I had put a lure on and nothing seemed to appear (by this I mean the pulsing ring around my character doesn't quite reach the ring of the Pokestop). Would this have any effect on me not seeing the Pokemon?