C++ lambda callbacks

I am trying to make an HTTP class, and I want to use C++11 (not C++14 yet) callbacks via lambdas. I have 2 mockups available, the first one works... but looks ugly. The second one I am aiming, is not compiling (error at the end).

I cannot use std::function, as this is an embedded project, and that template generates a lot of code.

#include <cstring>

class HTTP
{
public:
    void get1(const char* url, void* context, void (*callback)(void*, const char*) )
    {
        callback(context, "");
    }

    void get2(const char* url, void (*callback)(const char*) )
    {
        callback("");
    }
};

void test()
{
    int k;
    HTTP http;
    http.get1( "http://google.com", &k, [](void* context, const char* s){
        int *k = (int*) context;
        *k = strlen(s);
    });

    // this does not compile, looking for other alternatives
    http.get2( "http://google.com", [&k](const char* s){
        k = strlen(s);
    });
}

Error from gcc (xtensa-esp32-elf-g++ (crosstool-NG crosstool-ng-1.22.0-80-g6c4433a) 5.2.0)

HttpRequests.cpp: In function 'void test()':
HttpRequests.cpp:29:6: error: no matching function for call to 'HTTP::get2(const char [18], test()::<lambda(const char*)>)'
     });
      ^
HttpRequests.cpp:11:10: note: candidate: void HTTP::get2(const char*, void (*)(const char*))
     void get2(const char* url, void (*callback)(const char*) )
          ^
HttpRequests.cpp:11:10: note:   no known conversion for argument 2 from 'test()::<lambda(const char*)>' to 'void (*)(const char*)'