With tweetdeck you can create a timeline for anything (search result, your regular feed, list, someone’s post, only posts with > comments or whatever)
You just need to create one timeline for each list you want to see, then you are guaranteed than these timeline will only shows tweets belonging to the list and you won’t get any random tweet coming from Twitter suggestion.
If you want to test, you can do the same with regular Twitter, just create a list and then display your list, it works as well.
It just that when you start segmenting your tweet based on lists, you better use tweetdeck to display many side by side