My question is .... can bank use customers' deposit to lend? If so, what's the legal base to investigate the missing fund at MF Global? On the other hand, if banks are prohibited from using customers' fund for lending, where would the money come from for them (banks) to generate interest income?Thanks.

Think this depends on the legal structure. Often there is ring-fenced client money that cannot be lent (although it is sometimes when someone is keeping their eye on the ball).

Of course they can. That's the basic structure of most banks. The depositor lends money to the bank and the bank lends money to others for mortgages, car loans, business loans, etc. The government regulates this process (imperfectly) through reserve ratios (the bank can't lend out 100% of depositors money) and oversight on lending processes.The difference with MF Global is that the customers aren't lending money to MF Global when they put money in their account. In theory, MF Global is more like a warehouse that stores customers assets in segregated accounts and executes customer's instructions to move/trade those assets rather than a bank which borrows customer's assets and bundles that money for re-lending.