In the following, I tried to take into account all your constraints: filtering on fields of List, on fields of Item, counting items , and grouping by list.
The solution I see is that you could use values() (here is the django doc about this : http://docs.djangoproject.com/en/dev/topics/db/aggregation/#values)
from django.db.models import Count
lists = list(List.objects.filter(user=user))
items=Item.objects.values(list).filter(archived=False,list__in=lists).annotate(count=Count("id"))
#you will get a list of dicts of the form [{'count':2,'list':5},...] where 5 is the id of the list
#now, you can match you list with you item counts in python
list_items_count_dict={}
for item in items:
list_items_count_dict[item['list']]=item['count']
for list in lists :
list.item_count = list_items_count_dict.get(list.id)
That will make only 2 queries, one for getting the lists, the other for computing the item counts. Afterwards, you will have two loops (that could probably be replaced by list comprehension one-liners ), but only for the lists you are interested in.
afterwards, in your template, you can use
{{list.item_count}}
There might be a more elegant option, but that is what I have found right now. I am also certain that you could reduce the number of query to one by using custom sql.
Disclaimer: I have not tested this code, but I have tested similar code on similar models. You could have problems because list is one of the keyword of the Python language.