I use bitwarden. It's open source and works in browser and on phone. I haven't done any auditing myself, so I guess it's a leap of faith in that regard, but it's working great thus far.

It can import from a lastpass file.

Even though it's open source, there is a hosted instance (so the experience is much like lastpass). There was a kickstarter a while back that failed though, so I'm unsure how it's funded.