I do not use LastPass exactly because of what you describe. I use a KeePass Password safe without autofill. I use other software to sync the file. It used to be Dropbox, later I was using BitTorrent Sync, but what tool sync shouldn't really matter. As I see it: the tool only gets to see and sync an encrypted file. You could even use a USB stick and not sync at all. Or only sync on LANs.
I love it how I get to decide who or what gets to see the encrypted file.
Now hopefully the Keepass audit will not reveal any issues in the encryption.