In a way... yes. You can self-host it.
Basically this app is a node.js app built on top of the Crypton framework and is hosted on one of those servers, however, it doesn't have to be. You can have your own.
In both cases - the difference between Encryptr and every other app is that it works on zero-knowledge. I know it sounds just like another term, but it really is something awesome. The guys at Spideroak (Dropbox alternative, the one recommended by Edward Snowden himself as being the most secure and inaccessible to the NSA) really built something outstanding. The Crypton framework - which is, in simple terms - a way to store shit on a server without the server even knowing what it is.
Crypton has been audited 2 times and another audit is upcoming, see: https://crypton.io/docs/security/audits.html
Now, you can trust that audit, Spideroak and Snoweden, and go with that, or you can self-host it yourself, and have local copies.
I however, do not trust my technical expertise to be confident enough that I will build something more secure than what the guys at Spideroak are doing.
It's true, and the same still applies: don't store shit in the cloud if you want it private.
But there's a third way: If you find a way to store shit in the cloud without the server knowing what it is, as in, zero-knowledge (inherently strongly encrypted) then by all means, store it wherever you want.
The don't store it in the cloud thing only applies if your data can potentially be accessed by someone else, without your password. Dropbox for example, can look at any or all of your files at any time, without your password.
Other services that claim to be encrypted could, also, potentially make it 'unencrypted' for a short while, or for single users, or on request, for certain files.
The Crypton framework however stores data in such a way that it doesn't know what it is. There are no individual files, users, etc. All you have is a big lump of data, all of it fully encrypted, and portions of it can only be accessed with a secure password. You don't have the password, you don't access it, simple as that. The encryption is strong enough to withstand a global attack for thousands of years.
Crypton is open source and audited regularly. Any potential issues or vulnerabilities, old or new, are addressed.
For all intents and purposes, I think Crypton is much more secure than LastPass or others.
Not sure about Keepass because of the local files. It's not that I don't trust that the files are encrypted or secure enough, it's that I disagree with the idea of having to store them somewhere else, which is in itself potentially dangerous, and I disagree with the idea of actually having an individual file that is yours and yours only and can be known to only contain passwords.
I like the idea of security through obscurity much more.