How do I show the Applications Lens By Default?
Use the keyboard shortcut
I don't think there's a way to change the order of the Dash lenses without having to modify the source, but the easiest solution is to just use the keyboard shortcut: Super+A to directly open the Application lens.
Note: Super key = Win key
Customizing the keyboard shortcut
Open the application.lens file with:
gksudo gedit /usr/share/unity/lenses/applications/applications.lens
and on line 8, look for Shortcut=a.
You can change the a to any other letter to get a shortcut of Super+(letter).
What are Unity's keyboard and mouse shortcuts?