error: passing xxx as 'this' argument of xxx discards qualifiers

The objects in the std::set are stored as const StudentT. So when you try to call getId() with the const object the compiler detects a problem, mainly you're calling a non-const member function on const object which is not allowed because non-const member functions make NO PROMISE not to modify the object; so the compiler is going to make a safe assumption that getId() might attempt to modify the object but at the same time, it also notices that the object is const; so any attempt to modify the const object should be an error. Hence compiler generates an error message.

The solution is simple: make the functions const as:

int getId() const {
    return id;
}
string getName() const {
    return name;
}

This is necessary because now you can call getId() and getName() on const objects as:

void f(const StudentT & s)
{
     cout << s.getId();   //now okay, but error with your versions
     cout << s.getName(); //now okay, but error with your versions
}

As a sidenote, you should implement operator< as :

inline bool operator< (const StudentT & s1, const StudentT & s2)
{
    return  s1.getId() < s2.getId();
}

Note parameters are now const reference.

Member functions that do not modify the class instance should be declared as const:

int getId() const {
    return id;
}
string getName() const {
    return name;
}

Anytime you see "discards qualifiers", it's talking about const or volatile.