What time of year were you thinking? Keep in mind that Lac La Biche can get some pretty intense algae blooms in the summer which usually makes the fishing quite tough. The sooner you can get there when the season opens the better for fishing. Late May towards mid June. Won't need to worry as much about timing at Cold Lake but it seems to get better later in the season around August. But by this time Lac La Biche will likely not be worth it if we get another warm season.
At LLB there are cabins right on the water at the Sir Winston Churchill Provincial Park. They are next to the boat launch there. They are really sort-after though so you will need to book asap. Go to
https://shop.albertaparks.ca/ and select "comfort camping" at Sir Winston.