Lake Alta is high in The Remarkables, the spectacularly spikey 2,200 m west-facing mountain range overlooking Lake Wakatipu, with the north end immediately above Queenstown Airport. A ski field road with spectacular views from State Highway 6 just to the south of Franklin takes you to a parking area at 1,600 metres on the east side of the peaks.
From there, you can walk 1.7 km along the ski field road near the Alta chairlift. From the top of the lift, follow the cairns through the mountain wetlands over the ridge to Lake Alta. Allow about 40 minutes each way. In ski season, you can take the Alta chairlift most of the way up and hike the rest, although the lake will likely be frozen and snowed over.
If you have plenty of time and can pre-position a second car, you may want to continue on behind the Remarkables along the Wye Creek Route. This takes you up to a pass at 2,000 metres, immediately above Lake Alta. At the far end of the range, you can hike south to a series of waterfalls on Wye Creek South Branch, then down to a car park above Lake Wakatipu.
Remember that even in summer, it can be cold and changeable at these mountain altitudes. Check out NZMSC for advice on preparing for alpine conditions.
Thanks to Georgia (@the_cornishpixie) for the photos.