Often in treasury bills, as banks are too risky. Which is why treasury bill rates are so low, and the money does not get relent. Since Lehman's banks are not seen as safe and there is no deposit insurance for these large amounts.

The bank would be lending it out though.

What makes you think so? Interest offered by borrowers is generally low these days and risks are high. So lending isn't happening.

If that was the case, we would see M2 and M3 go up, and we aren't. Depending on how you want to measure it, you could even argue they are contracting slightly.

Looks like 'up' to me for M2: http://www.federalreserve.gov/releases/h6/current/ M3 not being tracked.

That said, I'm not entirely sure about the definition of M2 and how that's related to 'money sitting in the bank'. M2 includes 'savings and time deposits' according to Wikipedia, but it doesn't seem to differentiate whether banks in turn lend out that deposited money or it just sits there.