In general, it's best to avoid long query strings in GET requests. A great question for reference on this is the SO question What is the maximum length of a URL?. You don't want to exceed 2000 characters.
If your items will always fit in this length, you can use urllib.urlencode to convert your parameters:
>>> list1 = ["string1","string2","string3","string4"]
>>> list2 = ["domain_string1","domain_string2"]
>>> allparams = map(lambda x: ("list1", x), list1)
>>> allparams += map(lambda x: ("list2", x), list2)
>>> import urllib
>>> urllib.urlencode(allparams)
'list1=string1&list1=string2&list1=string3&list1=string4&list2=domain_string1&list2=domain_string2'
Instead, you could use a POST request. I highly recommend the requests library:
import requests
r = requests.post("http://127.0.0.1/search", data=allparams)