I own a Tundra and have been in your shoes. A carabiner will not work - not the right shape. If you don't use a lock, and a bear gets in, you are not in compliance with the manufacturer's specifications to make the cooler bear-proof. (If you care about that). A lock would also keep hobos out of your beer in the grocery store parking lot, restaurant, etc. (Won't prevent theft of the entire cooler.) Also, most likely of all, a lock will keep teenagers out of your beer in camp. If you are looking for your own off-brand padlock, fitting the lock is difficult, since you want no slop/slack. A few years ago at Home Depot, I found pair of Master locks, reasonably priced, keyed alike, that had shackles long enough and thin enough to fit. There was a little slop, so I cut a short spacer from plastic tubing to fill the gap. There is a risk of losing the key, so I bring a spare and so far no problems. I worry a little about rust jamming the innards of the lock but so far, so good. In known, serious, bear encounter country, I think I'd go with the locks, as they will, for sure, keep the lid closed.
I also think bolts work fine, and would probably keep the lid closed in the event of a bear encounter. Bolts may well be the better option. No key to lose, and easier to get the right, tight, fit. (Very easy to drop small metal parts into the river, though...) Track down hardware made of stainless or at least galvanized. Make it easy on yourself; use eye-bolts and wing-nuts, or some other combination that will not make you use tools every time you open the cooler. My bolts fit better with the nut on the bottom.
