Use of lambda expression in C++ ternary operator : error type mismatch

I am just exploring lambda expression and trying to use it to return from a function using C++ ternary operator. However the below code does not work with error!

this is a simplified version of the program to explain my actual problem so kindly post answer using a lambda only, not just return (x+y+offset).

In member function 'int Calculator::add(int, int)': 12:26: error: no match for ternary 'operator?:' (operand types are 'bool', 'int', and 'Calculator::add(int, int)::<lambda()>') 16:3: warning: control reaches end of non-void function [-Wreturn-type]

    #include <iostream>
    #include <string>
    
    class Calculator
    {
      public:
      bool initalized = false;
      int offset = 0;
      
      int add(int x, int y)
      {
          return !initalized ? -1 : [this, x, y]()
          {
              return ((x+y) + offset);
          };
      }
    };
    
    int main()
    {
        Calculator c;
        c.initalized = true;
        c.offset = 1;
    
        printf("%d", c.add(2,10));
    }

What am I doing wrong here?