Can I take a well known song and alter it (basically, make it lullaby style) and then use it in a short I'm making without worrying about licensing fees?
In a word, no. If you merely produce a different arrangement of an existing copyrighted work, that arrangement is a so-called "derivative" work and is subject to the original author's copyright. There are certain narrow rights to use existing works for the purpose of parody, but those rights would not apply in your situation. You should consult an intellectual property lawyer before you go forward.
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