This is a wonderful hike. The first time I hiked up to the Tea House was within the first year I arrived in Calgary. It was work. I had been living at sea level for most of my life and the elevation was a killer. Yesterday's up from Lake Louise wasn't that difficult at all by comparison. Depending on the time of year that you do this hike - bring layers. It was much colder at the top. It was actually kind of blizzardy for a bit. We prefer the slightly cooler weather for hiking. When you are doing fairly steep climbs and working your body warms up. When it is very warm or even sometimes moderately warm you can get to hot very quickly. Always have plenty of water. And always prepare for longer hikes in case there are problems. I know this sounds a bit silly to some but we got caught in a blizzard and it was June 21st - it only lasted 2-30 minutes or so but could easily have lasted 3 hours.
Have fun and be safe.