Lake Mackenzie is part of the Routburn Track. To accomplish this hike in one day, you will start by parking at the Divide (Milford Sound side of the Routeburn Track) and hiking 12km one way. Stop at the lake, go for a swim, have a snack and make your return back to your car. This is a well maintained trail with a few slippery sections, and is manageable in one day for those who are experienced hikers.