Simple Web Crawler for Small Sites
I have made some changes to make it neater and more efficient. See the end of this response for the final solution. But I'll start with a few comments.

There is no point making your class inherit the object class, especially if you're working with Python 3.

class Page(object):


The soup() method seems to be called indiscriminately causing BeautifulSoup to parse the contents of the page in concern too many times (see the map_page() method, for example). It is probably more efficient to parse once, afterwhich you can save whatever (e.g. title and links)you need as object properties.

Using list and map in this context seems unnecessary. It helps if you strive for readability --- your future self will thank you.

links = [i for i in (list(map((lambda url : url if bool(urlparse(url).netloc) == True else urljoin (self.base_url, url)),href))) if i.startswith(self.base_url)]


Also, checking the truthiness of urlparse(url).netloc doesn't require you to coerce it to a boolean result first. Simply replacing if bool(urlparse(url).netloc) with if urlparse(url).netloc would suffice.

In the site_map() function, you can replace the while loop with something simpler, e.g.:

while links_to_map:
    check_and_add(links_to_map.pop())


I have also made other subjective simplifications that hopefully should be obvious to you.

import pprint
import urllib.request
from pprint import pprint
from urllib.parse import urlparse, urljoin

import bs4 as bs


class Page:
    def __init__(self, base_url, url):
        self.url = url
        self.base_url = base_url
        self.souped = None
        self.title = None
        self.links = None

    def soup(self):
        def clean(url):
            return url if urlparse(url).netloc else urljoin(self.base_url, url)

    sauce = urllib.request.urlopen(self.url).read()
    self.souped = bs.BeautifulSoup(sauce, "lxml")
    self.title = self.souped.title.string
    hrefs = set([clean(i.get("href")) for i in self.souped.findAll("a")])
    self.links = [link for link in hrefs if link.startswith(self.base_url)]
    return self

    @property
    def map_page(self):
        lookup = {self.url: {"title": self.title, "links": self.links}}
        return lookup


def site_map(base_url):
    map_pages = {}
    links_to_map = [base_url]

    def check_and_add(url):
    if url not in map_pages:
        page = Page(base_url, url).soup()
        links_to_map.extend(page.links)
        map_pages.update(page.map_page)

    while links_to_map:
        check_and_add(links_to_map.pop())

    pprint(map_pages)