No, because if you encrypt your own material you hold the keys. If you let someone else do it, they hold the keys. And who knows how good they are at keeping them safe.
You always know how good you are (or, how bad you are) at keeping your own keys safe.
Keepass(x), gpg encrypted file backup with the gpg keys backed up on a CD in a bank safety deposit box. (and if you're daring, a copy of the key on a usb jump drive you keep on your person at all times)
Don't forget the copy you keep in your head and enter whenever you need to access the safe; you're vulnerable at that point to a key logger. :)
With LastPass, you encrypt your own material, LastPass never holds the keys. LastPass works exactly the same as KeePass: there's a binary blob that is kept on an Internet-accessible server, and you download the blob and decrypt it locally. All they have is an encrypted version of your key, just like in your Linux/Mac/Windows desktop system. Yeah, maybe they could have used different keys for their web site and the blob, but I don't see how that would increase security all that much. With either service, an attacker has to get your blob (by hacking the LastPass server or your computer's cache, or by finding the KeePass blob on your computer or in a Dropbox or similar cloud-based server), then they have to brute force the key. If your key is easy to figure out using a dictionary, then you're hosed no matter which service you use.
This is similar to the Gawker attack, except with Gawker the encrypted passwords were made public, along with the subset that were brute forced. I checked for my email address and it only showed up in the first list, not the second. Of course, my passwords for everywhere use the "at least one letter, number and special character" rule, they are generally fairly long (pre-Gawker, 8 characters, post-Gawker, 14), and I don't use leet-speak to determine the non-alpha characters (leet-speak increases the effort needed to brute-force by only a small factor).