Auxiliary variables are useful for giving per instance scoped variables to the lambda and it's also the only way to move data inside the lambda. i.e. something like (notice the semi-colons):

string str = "asdfasdfasdfasdfasdfasdf";
string s2;

[&; auto s = move(str); const size_t n = s.length()*4] {
s2 += s;
s2.resize(n, '!');
}();

cout << str << endl << s2 << endl;

This example gets treated as if you wrote:

struct gensym {
string &s2;
mutable string s;
const size_t n;

bleh(string &s2, const string &str) :
s2(s2), s(move(str)), n(s.length()*4)
{}

void operator() const
{
s2 += s;
s2.resize(n, '!');
}
};

string str = "asdfasdfasdfasdfasdfasdf";
string s2;

gensym(s2, str)();

cout << str << endl << s2 << endl;