The Optimum Strategies
Your optimum strategy has two parts: You start by rowing directly away from the goblin. As he pursues you, you turn so as to always keep the center of the lake between you and the goblin. You can maintain this strategy until you are 1/K times the radius of the lake (R) from its center and the path you row will be a semicircle. The second part of your flight is to continue in a straight line tangent to the circle in which you were rowing. (check the image)
The optimum strategy for the goblin (if you also adopt the optimum strategy) is to run as fast as he can in one direction around the lake. If you abandon your optimum strategy before you reach the the R/K circle, the goblin simply reverses direction as necessary to minimize your advantage. Regardless, the goblin can do no better than being as far away as possible when you cross the R/K circle. After you cross the R/K circle and are following the tangent to the shore, if the goblin reverses direction, you simply turn onto the chord centered on your position and head away from the goblin; you will reach the shore with an even greater margin.
The Answer
The threshhold value of K is 4.60333885 (to 8 decimal places). This is the solution to:
sqrt(1-1/k^2) = (pi + acos(1/k))/k.
The left side of the equation is the time you need to travel along the tangent line (for R = 1, and speed = 1) and the right side is the time for the goblin to arrive at the same point (speed = K).