C++ — Why can’t a const mutable lambda with an auto& parameter be invoked?

Example:

#include <type_traits>

int main()
{
    auto f1 = [](auto&) mutable {};
    static_assert(std::is_invocable_v<decltype(f1), int&>); // ok

    auto const f2 = [](auto&) {};
    static_assert(std::is_invocable_v<decltype(f2), int&>); // ok

    auto const f3 = [](auto&) mutable {};
    static_assert(std::is_invocable_v<decltype(f3), int&>); // failed
}

There are two interesting things here.