"function local static function-object that's initialized by lambda, thread-safe or not?" Code Answer
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not only is it not thread safe, it doesn't do what you want.
by defining the lambda as static, it captures (by reference) the array passed in the first time it's called. further calls continue to reference the original array, regardless of which array is passed in.
when the first array goes out of scope, further calls will invoke ub, as it now has a dangling reference.
edit: an example http://ideone.com/kccav
note, even if you captured by value, you'd still have a problem because it would still only capture the first time you invoke the function. you wouldn't have the dangling pointer, but it still would only initialize the copy the first time.