This is presumably obvious, but if one is going to use something like Dropbox or Google Drive, you're kind of defeating the point of not using the cloud. I'm comfortable enough with how Lastpass handles the encryption to put up with the potential minor risk for the extra convenience of the syncing and such just working. At some point, each of us has to decide that the risk is low enough that we're comfortable with what we pick.
I partly agree, which was why I didn't recommend that route first, but it's very misleading to say it's defeating the point because the two scenarios are not equivalently secure.
If you use a keyfile with keepass and sync your password database with dropbox (I specifically mentioned using a keyfile in that case), it actually has significant security advantages over using a cloud-based password manager. Setting aside the issue of trusting someone else to actually keep your data safely encrypted (let's assume you can trust Lastpass to not deliberately do anything wrong), you can access your lastpass database through their website (or at least one could when I used the service). That means all someone needs is your password to access the database. So even if Lastpass is doing everything right in their client and plugins (which we're assuming, but in real life is still an "if"), someone who breaches their servers (which has happened once, although it's not clear if they got password databases) just needs to figure out the password.
If you use a separate keyfile with Keepass that you keep locally, and then put your database on Dropbox, someone who breaches your Dropbox cannot usefully breach the database because they lack both the decryption key *and* your password. Even if they knew your password, it would do them no good without the keyfile. The keyfile needs to only be made and sent to your devices once, only the database needs to be synced regularly, so you can keep the keyfile local-only and get some of that cloud convenience with very little loss of security. Keepass also does all the encryption locally, so Dropbox doesn't even have the chance to see your unencrypted data.
That said I still do all my file syncing myself, because, as you suggest, any external cloud involvement is more than I'd like. I don't recommend Dropbox or Google drive for hosting your own password database, but they can be used in a way that has security advantages over a pure cloud solution.