First, if people didn't believe that BTC protects from double spend, then it would not be used by anybody. Secondly, the whole point of the proof of work scheme is that it's impossible, or at least extraordinarily costly, for anyone to outrun the main chain enough to publish a new block that replaces blocks from a week ago. It's in fact considered impossible for blocks from an hour or so ago.

So, assuming the BBQ supplier waited about an hour for confirmation, the chance that the money would be lost is minuscule with BTC transactions. With Lightning transactions, the same is not true at all - the customer could close their channel abruptly two months later when the BBQ joint is on vacation, and the money would suddenly vanish forever (assuming they don't catch the fraud in the time window before it becomes permanent).

Of course, in both cases, if you're the person who sent the money and the BBQ never arrived, you're out of luck entirely. Which is why the claim that BTC or Lightning enable trustless monetary transactions is mostly bogus, even with a no-double-spend guarantee. And waiting one hour for a payment to a BBQ joint to clear is basically unworkable (and the reality is more like two hours - one hour for the transaction to make it to be mined, and the other hour to confirm the block where it was included remains permanent).