If you use/make a custom layout you can. One of the things you can check for is the state of the current page and whether someone is logged in or not. So you could potentially have many different looks for your friends pages, your pages and still different again if someone is viewing those pages but not logged in, etc.
The easiest thing to do is pick a custom layout, such as component or boxy or whatever and find the associated "help" community on LJ. They'll have tutorials, etc.
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For component it's
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