There are no websites I believe that could lend you BTC's and here is only forums allows to you lend money on behalf your account may be collaterol.
How many Bitcoins do you need and the lending owner will give you depending upon your account membership.
There are too many websites offers lending services of course with valid collateral not "collaterol". And I bet the service requires KYC policies on some websites. But if you will refer on lending section on this forum (link posted above) then every lender have its own rules to be followed.
I seen here in forums as the lender require account if we didn't pay back, but what does this lender will do when we wont pay back?
I checked last time their is site where we get the current value of our account in someone lending thread.
Those sites require some proof might be KYC documents as you said (KYC policies), but it all require some time for verification.
I am new to this field and readed few threads in the past regarding lending money, but few of them made red trust to the on posters for asking a loan.
I suggest the OP to read the subforums to meet right person for lending a loan.
Edit:
Try aTriz Loan service as he is good with his services.
[Collateral Not Required]https://bitcointalk.org/index.php?topic=2275651.0