If the population of Canadian lynx were to completely disappear, the most likely response would be:
The population of snowshoe hare would outgrow the food supply, so there would be less food available.
Without the predatory pressure from the lynx, the snowshoe hare population would likely increase significantly since there would be fewer natural checks on their population. This rapid increase could lead to overgrazing of their food sources, ultimately resulting in a depletion of available food.