There is no defined walking trail that goes right around Lake Louise. The Lakeshore Trail is an easy there-and-back 4 kilometer (or 2.4 mile) paved trail that starts at the public parking lot near Chateau Lake Louise and follows the Lake Louise’s north shore (the right hand side) to the back of the lake.
From there, there are spectacular views back across the water towards Chateau Lake Louise. The total round trip should take around 2 hours and early morning is the best time to find a parking spot and avoid the crowds.