Start subthread with arbitrary function including parameters

I would like to build a function, which checks if a subthread is already ruing and if not, start a subthread with any function and paramter given. As multithreading tool I use this post: Is there any way to kill a Thread in Python?

The idea so far is the following:

from ThreadEx import ThreadEx

class MyClass:
    def __init__(self):
        self.__Thread = ThreadEx(name='MyClass',target="")
        self.GlobalVariable = "MyClass Variable"

    def SubThread(self, function): 
        if not self.__Thread.is_alive():
            print("Thread is not alive")
            self.__Thread = ThreadEx(target=function(),args=(self,))
            print("Thread is going to start")
            self.__Thread.start()
            print("Thread started")
        else:
            print("There is already a subthread ruing")

    def MyFunction1(self, argument1, argument2, argument3):
        self.SubThread(lambda: MyFunction1(self, argument1,argument2,argument3))

    def MyFunction2(self, argument1, argument2):
        self.SubThread(lambda: MyFunction2,argument1,argument2)


def MyFunction1(self, argument1, argument2, argument3):
    print(self.GlobalVariable)
    print("MyFunction1")
    print("Argument1: " + str(argument1))
    print("Argument2: " + str(argument2))
    print("Argument3: " + str(argument3))

def MyFunction2(argument1, argument2):
    print("MyFunction2")
    print("Argument1: " + str(argument1))
    print("Argument2: " + str(argument2))

unfortunately if I execute:

from Myclass import MyClass

self.MyClass = MyClass()
self.MyClass.MyFunction1("Test1","Test2","Test3")

The output is:

Thread is not alive
MyClass Variable
MyFunction1
Argument1: Test1
Argument2: Test2
Argument3: Test3
Thread is going to start
Thread started

So the function is executed before the thread starts. So my question is, how do I send MyFunction including all arguments to a subthread and being able to repeat this with any other function without write a routine each time. I was already looking for *args and **kwargs but I couldn't find the right syntax or it was the wrong way.

Thanks in advance! :)