I have created such Enum object:

class Gender(Enum):
    FEMALE = 'female'
    MALE = 'male'
    RANDOM = random.choice([FEMALE, MALE])

and i want to get really random value each time, but it does not work:

>>> class Gender(Enum):
...    MALE = 'male'
...    FEMALE = 'female'
...    RANDOM = choice([MALE, FEMALE])
... 
>>> Gender.RANDOM
<Gender.MALE: 'male'>
>>> Gender.RANDOM
<Gender.MALE: 'male'>
>>> Gender.RANDOM
<Gender.MALE: 'male'>
>>> Gender.RANDOM
<Gender.MALE: 'male'>

I have also tried use lambda, but it's looks not so good, although it works:

Gender.RANDOM()

Are there other way to get random values each time, without using lambda expressions?

We use this enum object as default value of the argument of the some method that's why it should be an attribute, not a function, because when we use Gender.FEMALE it is not a function, it's an attribute and Gender.RANDOM should be an attribute too:

def full_name(gender=Gender.FEMALE):
    ...


def full_name(gender=Gender.RANDOM):
    ...

I tried a way with metaclasses. And it works!

import random
import enum
class RANDOM_ATTR(enum.EnumMeta):
    @property
    def RANDOM(self):
        return random.choice([Gender.MALE, Gender.FEMALE])


class Gender(enum.Enum,metaclass=RANDOM_ATTR): #this syntax works for python3 only
    FEMALE = 'female'
    MALE = 'male'


print(Gender.RANDOM)   #prints male or female randomly

Here by making RANDOM_ATTR the metaclass of Gender, Gender is like an object of class RANDOM_ATTR, so Gender has the property RANDOM.

However,the below code you described in your question doesn't work the way you expect.

def full_name(gender=Gender.RANDOM):
    ...

The RANDOM property will be called only once. To know why, please read this answer. Default arguments are like attributes to function, which will be initialised only once.

For that i would suggest you do something like this:

def full_name(gender=None):
    gender = gender or Gender.RANDOM
    ...