It could also mean that at some point in time you will suddenly achieve infinite enlightenment, but immediately afterwards you will fall back to the normal level of your mundane existence, with no lasting effect from your experience.
Seriously though, "asymptotically speaking" could be fairly straightforward in the right context - such as one where some mathematical function is under discussion. Prefereably one that actually has, well, an asymptote.
What was the lecture about?