It depends on the type of lettuce you're growing, but I'd say when it gets over 85 to 90 degrees for most. Romaine lettuce handles the heat very well; I've grown it in temps in the high 90s to over 100 and it never bolted, but most leaf type lettuces will bolt before that. In Minnesota you may not have to worry too much about it.
A 12 inch deep pot should be enough. Most lettuce can stand part shade, but still needs quite a bit of sun. I'm not sure about pests in your area, but if you plant it in good soil, keep it watered when needed and so on, you shouldn't have trouble with bugs. Bugs are attracted to stressed plants. Rabbits will eat it, of course and sometimes birds will take bites of it.