The most important reason why they must contain only one method, is that confusion is easily possible otherwise. If multiple methods were allowed in the interface, which method should a lambda pick if the argument lists are the same ?

interface TestInterface {
    void first();
    void second(); // this is only distinguished from first() by method name
    String third(); // maybe you could say in this instance "well the return type is different"
    Object fourth(); // but a String is an Object, too !
}

void test() {
    // which method are you implementing, first or second ?
    TestInterface a = () -> System.out.println("Ido mein ado mein");
    // which method are you implementing, third or fourth ?
    TestInterface b = () -> "Ido mein ado mein";
}