Earlier quoted context omitted.
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…
Lastpass also only syncs data after it's encrypted locally, so the threat model is the same.
This matters because even if it's client-side encryption, the encryption code just got downloaded when you opened the site so if the server or the network was compromised, you got compromised. [0]
With Keepass, the only time you run that risk is when you download Keepass.
[0] As far as I can tell, this is the core argument of tptacek's "javascript crypto considered harmful" rant (https://www.nccgroup.trust/us/about-us/newsroom-and-events/b...). I'm not sure, because it's written worse than his most drunken HN comment, but I believe it is.