The relative clause can (and should) be omitted if it doesn't add meaning, information or clarity to the sentence.
The book you lent me, which I never read before, was very good. The non-restrictive relative clause (introduced by which) adds information that is not essential to the meaning of the sentence.
I lost the book that you lent me. This restrictive relative clause (introduced by that ) is essential to the meaning of thiis sentence.
In your examples (a) is the best sentence. The others are not ungrammatical, just not as good as (a).
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