Lens is just a static ability, meaning you can look whenever. What you can not do is interrupt countrysides crusher. The "look at the top card" ability of Lens doesn't use the stack.
So your answer your question directly: It doesn't stack, you cant shuffle in between.
January 9, 2017 3:44 a.m.
This seems more fit for the Rules Q&A section of the forum. You can find it on the tab at the top.
January 9, 2017 4:36 a.m.
Countryside Crusher will pretty much have you put cards into your graveyard until you reveal a non-land card. This last card will remain on top of your library after being revealed. This whole process is a single ability that's resolving, as you repeat the process as part of the original ability.
All that Lens of Clarity will do for you specifically in this case is knowing whether you will get at least one +1/+1 counter on the Crusher or not, should the card that's on top of your library at any point prior to the Crusher's ability resolving stay where it is.
It will allow you to look at the top card at any point in time, so technically, you will know what card will be revealed next before you actually have to reveal them. However, since no player receives priority while an ability is resolving, you won't be able to do much with this information, as you'll have to wait until the ability has finished resolving.
January 9, 2017 10:18 a.m.
BlueScope seems to have completely covered it - if that answered your question, mark that as the answer.