Obviously with lending on small scales, such as that which takes place on this forum, the lender takes bitcoin from their holdings/reserves, and sends it to the borrower's address. However, when banks lend fiat to individuals or to businesses, it's not a case of them taking any fiat from their holdings/reserves and putting it in to the borrower's account. Generally when banks give out a loan, they simultaneously create a new credit and a new debit of the same amount. New money is created out of thin air, and the bank doesn't need to move any money from their reserves, or even have enough money in their reserves to cover the loan if they wanted to.
This credit theory of money, while possible with a monetary system such as fiat where more can be created at will by centralized entities, isn't possible with a system like bitcoin. If a central entity wanted to lend out bitcoin, they would have to have the bitcoin to actually lend out. A fractional reserve system would be possible, although probably with a much larger fraction in reserve than commonly occurs in fiat banking. I for one would never let a third party store a fraction of my bitcoin whilst lending the rest out, but given the number of users who seem quite happy to hand over complete control of their coins to web wallets and exchanges, I have no doubt a fractional reserve system could exist.
If we put the credit theory here and if bitcoin reserves would lend out bitcoin to other then that must create new bitcoins out of thin air but that is again impossible.
So the total idea of lending in the same way fails right here. Just imagine how would lending work id they had out lend gold. Not money based on gold but actual gold.
Reserves would have to give out actual gold and that would not create new gold out of thin air. Although new gold can be mined but then there is a limited supply to gold, we just don't know how much.
As for the large scale bitcoin lending, well it might be possible in some way, probably huge collaterals based on trusted entities and escrows.
Even that would only be possible if bitcoin is trusted and accepted as a legal currency.