When you are not attached to your company's network and want to work with your local replicas, you will need to follow a couple of steps to tell Lotus Notes that you are offline.
Click on Office at the bottom-right-hand corner. Location options will appear.
Click on Island (Disconnected). The location field will change to Island.
Hover your mouse over the Mail Bookmark. Notice that the status bar reads "Mail is on Local."
Click on the Mail Bookmark. Your local replica of your e-mail will open.
Notice that the blue line at the bottom left now reads "Local."
You could also open your Calendar or To Do Items. They are also now replicated locally so that you can work with them offline.
The Contact list or Personal Address Book is already a local database and does not need to be replicated to be available for when you are offline.