Why C++ lambda is slower than ordinary function when called multiple times?

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It turned out that this is not an issue with lambda expressions, just that the compiler optimized-out the outer loop in the first case by caching the result of the sum() function.

After changing the first case to this form:

out = 0.0;
for (size_t i = 0; i < MAX; ++i)
{
    out += sum(v);
    v[i] = 1.0; // this adds O(1) time and prevents caching
}

in both cases the timings are approximately equal, with the lambda as a favourite.

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