While I like the idea of using LastPass, I think the danger lies at wherever your weakest link is, and the moment you choose to index your passwords somewhere other than your brain, you are creating the potential for a weakness.

Specifically, if someone gains access to your physical computer and they figure out your LastPass password, what happens next?

If you choose to use LastPass, make sure you do it with a fantastically long, entirely random password.

Example: "3BA^h<VQgj+nL%KP$ (this was completely randomly generated at http://passwordsgenerator.net/)

For a little reasoning, look into how passwords are generally hacked. Usually, hackable passwords consist of words or l33t words (l!k3 th!5) that are somewhat related to the person. A massive number of people use the same words or patterns for these things, so a brute force attack informed by a l33t-smart dictionary (minus the definitions) often is the cause for a hack like this. Furthermore, in different languages, there are more frequently used letters and spelling conventions, which can inform the dictionary's ordering or choice of words. (Think: colour vs color)

However, if the person does indeed use a random sequence of characters, the average person doesn't usually go outside the alphanumeric range. If the password is only lowercase, that's 32 characters. If it contains uppercase, that's 62 characters.

So then, we can take that information and use it to understand the complexity of a brute force algorithm based on possible permutations and other info.

Take a look at this: http://www.passwordmeter.com/

(Disclaimer: I do not hold any type of CS degree or formal training in cryptography. I've listened to a few classes online though.)