How Can I use Null Lambda in C++?

In this particular case, you can just define your null closure as one that always returns -1:

template <typename Lambda>
int foo(Lambda bar) {
    return bar(3);
}

#include <iostream>
int main() {
    auto const NULL_LAMBDA = [](int){ return -1; };
    std::cout << foo([](int a) {return a + 3;}) << std::endl;
    std::cout << foo(NULL_LAMBDA) << std::endl;
}

The likelihood is that if you're selecting at run-time which implementation to pass, then you're much better off type-erasing it with std::function rather than instantiating templates. And a std::function is permitted to be empty - it can be assigned from and compared against a null pointer.

---

If you know at compilation time that some call sites will always pass the 'null' lambda, then you can specialise the implementation appropriately. Obvious options include overloading foo() with a version that doesn't take the bar argument, or specializing it with a different implementation when bar is not a callable.

If much of foo() is common to both kinds of invocation (perhaps it has a lot of side effects, and bar() is provided as a callback?), then you might be able to conditionalise the optional part using std::is_same<>. This requires if constexpr, as the lambda is not callable as bar(3):

static auto const NULL_LAMBDA = nullptr;

#include <type_traits>
template <typename Lambda>
int foo(Lambda bar) {
    if constexpr (std::is_same<decltype(bar), std::nullptr_t>::value)
        return -1;
    else
        return bar(3);
}

#include <iostream>
int main() {
    std::cout << foo([](int a) {return a + 3;}) << std::endl;
    std::cout << foo(NULL_LAMBDA) << std::endl;
}

You can add a dedicated specialization:

#include <iostream>
#include <cstddef>

template<typename Lambda> int
foo(Lambda bar)
{
    return(bar(3));
}

template<> int
foo<::std::nullptr_t>(::std::nullptr_t)
{
    return(-1);
}

int main()
{
    ::std::cout << foo([] (int a) -> int {return(a + 3);}) << ::std::endl;
    ::std::cout << foo(nullptr) << ::std::endl;
}