Lion and man with visibility in monotone polygons

In the original version of the lion and man game, a lion tries to capture a man who is trying to escape in a circular arena. The players have equal speeds. They can observe each other at all times. We study a new variant of the game in which the lion has only line-of-sight visibility. That is it can observe the man's position only if the line segment connecting them does not intersect the boundary. We show that despite this limitation, the lion can capture the man in any monotone polygon in finite time.