Okay, this is hilarious. That's exactly what my first answer was. But it's not the "true" answer, because it boils down to semantics (or limits, if you prefer).
Turns out I told it correctly: https://puzzling.stackexchange.com/questions/2155/the-lake-monster wasoxygen found it on StackExchange.
Wow, okay, so I didn't even tell the question right but you still got the answer. The gist of it, I think, is that you can row 1 radius and the monster can run 4r and so you need to "shorten the circle" by rowing to r/4, whereupon you can move around the circle faster than the monster can run. I believe. That was roughly my solution (after I sugged 8bit's everlasting spiral) and my friend said I got it, but I may be mixing up the details. I'll try to get back to you with the actual question.