I had the same problem with LB - I knew there were things that needed to be done that weren't high on the list. The reason this happens is that item positions on the list are purely a function of their priority, and due dates can only reduce priority, not increase it.
As an example, if I have "have football & beer evening" in at a reasonably low priority, and the last item is "buy beer on sat morning", buying the beer will be low on the list, but I really need to buy the beer! The solution would appear to be that I should increase the priority of the parent nodes, however this is a) time consuming, and b) will have knock on impacts on siblings, aunts, and uncles of my beer evening node.
So, you are left with two options - remember the urgent items separately or spend 1/2 hour fiddling with priorities when a situation like this develops. I instead went with the GTD system using Palm calendar for hard landscape, Palm todo for Next Actions, and Natara Bonsai for Projects and Someday/Maybe.
There are ways to make LB work - it has a lot of happy users. It's not for me though...
Regards,
Tony