Can a lyrics web site be legal, assuming there are no special agreements with the artists?
Is publishing song lyrics considered "fair use?"
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Generally, no - lyrics of a song are intellectual property, and the mere act of publishing them, especially if commercialised through advertisements, can be grounds for a claim of copyright infringement to be brought against the website operators.
For example, in 2012, a company that displayed websites without a license from the rightsholders was awarded $6.6 million in statutory damages and legal costs.
As for whether it is fair use, it will depend on the precise circumstances. The mere publishing of the lyrics without license is unlikely to be considered fair use - in general, it must educate, or stimulate creativity.