Not entirely, since you download the encryption code way more often (for example, when you open the "Lastpass Vault", which is just a website like any other). Parts of Lastpass are simply a website, not part of the browser extension, and as an avid Lastpass user in all honesty I don't know which parts.
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.
