Update: May 18th, 2018 - Dogs and other domestic pets are now prohibited and this will be enforced by park rangers year-round.
Last year, Joffre Lakes Provincial Park had 3,891 campers and 157,215 day-use visitors, of which 60% made the strenuous hike to the second of the three lakes in the park.
BC Parks allows dogs in many provincial parks, including nearby Alice Lake, but domestic animals are restricted from beaches and day-use areas, public buildings and other sensitive areas where signs are posted. In the areas where dogs are allowed, owners are required to clean up after their pets and must control the animal at all times so they do not impact the park environment.
While this policy hasn't gone into effect yet, it will ahead of the busy summer season. B.C. Parks will issue a more formal statement at that time.
Image from B.C Park's website.