Only the first is correct.
1. I will lend you the book as soon as I have done with it.
2. I will lend you the book as soon as I will have done with it.
Are the both grammatical?
Only the first is correct.
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You will also hear "I will lend you the book as soon as I am done with it".
Remember - correct capitalisation, punctuation and spacing make posts much easier to read.
"...... as soon as I am done with it." seems to be the most appropriate.
Context is important. Please provide enough for us to be able to deal effectively with your question.
Your thread title should include all or part of the word/phrase being discussed.
If you just want to know the meaning of a word, try OneLook Dictionary Search first.
I wouldn't say either "I have done with it" or "I am done with it".
Nor would I, but you'll hear both. I, too, would say "I'll lend you the book when I've finished with it".
Remember - correct capitalisation, punctuation and spacing make posts much easier to read.
I would say "am done with it."
I would not say "have done with it." It makes me want to ask "have done what with it?"