check if an IP is within a range of CIDR in Python

In Python 3.3 and later, you should be using the ipaddress module.

from ipaddress import ip_network, ip_address

net = ip_network("1.1.0.0/16")
print(ip_address("1.1.2.2") in net)    # True

You can't really do string comparisons on a dot separated list of numbers because your test will simply fail on input say 1.1.99.99 as '9' is simply greater than '2'

>>> '1.1.99.99' < '1.1.255.255'
False

So instead you can convert the input into tuples of integers through comprehension expression

def convert_ipv4(ip):
    return tuple(int(n) for n in ip.split('.'))

Note the lack of type checking, but if your input is a proper IP address it will be fine. Since you have a 2-tuple of IP addresses, you can create a function that takes both start and end as argument, pass that tuple in through argument list, and return that with just one statement (as Python allows chaining of comparisons). Perhaps like:

def check_ipv4_in(addr, start, end):
    return convert_ipv4(start) < convert_ipv4(addr) < convert_ipv4(end)

Test it out.

>>> ip_range = ('1.1.0.0', '1.1.255.255')
>>> check_ipv4_in('1.1.99.99', *ip_range)
True

With this method you can lazily expand it to IPv6, though the conversion to and from hex (instead of int) will be needed instead.