"NTLM authenticates the connection, not single requests", according to the requests_ntlm package's source code. This means that you either have to reuse the same request or keep authenticating with each request you make.
You should be able to use requests' Session object to get a persistent connection that you can reuse, as well as making it easier to set the authentication. The following code demonstrates what is going on and should provide something for you to build on:
import requests
from requests_ntlm import HttpNtlmAuth
username = 'myUser'
password = 'myPswd'
url = 'https://NTLMwebsite/base.com'
nextPage = 'https://NTLMwebsite/base/next.com'
s = requests.Session()
s.auth = HttpNtlmAuth(username, password)
r1 = s.get(url)
r2 = s.get(nextPage)
print 'r1', r1
print 'r2', r2
print 'Session using same connection:', r1.connection == r2.connection
r1 = requests.get(url, auth=HTTPBasicAuth(username, password))
r2 = requests.get(nextPage, auth=HTTPBasicAuth(username, password))
print 'r1', r1
print 'r2', r2
print 'Non Session using same connection:', r1.connection == r2.connection