for user in lst:
    if a == user['first_name']:
        print "%s detected" % a
        break
else:
    print "%s not detected" % a

>>> lst = [
...     {
...         "first_name": "Ivan",
...         "last_name": "Ivanov",
...         "middle_name": "Ivanovich",
...         "note": ['yes', 'my', 'fantasy', 'is', 'perfect']
...     },
...     {
...         "first_name": "Andrey",
...         "last_name": "Andreenko",
...         "middle_name": "Andreevich",
...         "note": ['and', 'my', 'too']
...     }
... ]
>>> 
>>> a = 'Andrey'
>>> 
>>> def search_user(name):
...     return name in tuple(i['first_name'] for i in lst)
... 
>>> if search_user(a):
...     print('found')
... else:
...     print('not found')
... 
found
>>>

return name in set(i['first_name'] for i in lst)