This fascinating argument is developed in John Hudson's recent article, "Amelia Bassano Lanier: A New Paradigm." While initially inclined to reject the notion without much deliberation, I must confess that I found the argument quite intriguing and far more plausible than those put forward for any of the other "usual suspects" (e.g., Bacon, de Vere, Marlowe, et al.).
So many little details arise in support of Hudson's hypothesis, including the following: (1) Amelia was the mistress of the Lord Chamberlain, who became patron of the Lord Chamberlain's Men shortly thereafter. (2) Several of her relatives held prominent posts related to both set design and music. (3) Dedications to The Rape of Lucrece and Venus and Adonis went to the Earl of Southampton, a neighbor and close friend of Amelia. (4) Ben Jonson (who claimed to know the author of the plays) strangely compared said author to a "matron" in the First Folio. Finally, (5) unlike most of the other "suspects" (with Marlowe perhaps the most notable exception), Amelia was an accomplished and published poet.
It's a long article with far more than the above, and well worth perusal. Those interested can find it here: http://shakespeareoxfordfellowship.org/wp-content/uploads/Oxfordian2009_Hudson_Bassano.pdf.