Banff has two peak seasons: the summer tourist rush from July through August and the winter ski season from December through January (particularly around Christmas break). As with most travel destinations, the shoulder seasons (spring and fall) are best for avoiding crowds.
Lake Louise itself is 61 km from the Town of Banff. The drive takes about 45 minutes along the TransCanada or an hour if you drive the scenic Bow Valley Parkway.
When you have enough layers for your upper body, your lower body shouldn't get cold, even if you're wearing shorts. You can always wear shorts during the summer in Banff, especially during a long hike. If the weather forecast looks questionable, wear hiking pants or leggings.