Find the average number of n:m connections of two tables?
I have no idea which RDBMS you are using, but on SQL Server using CTEs (Common Table Expression) it might look like something similar: 

with tbl_count (user_id, nboflists) as 
(
   select user_id, count(list_id)
   from lists_users
   group by user_id
)
select avg(nboflists)
from tbl_count


There must also be dozen of other (better?) ways  of doing this...