I don't trust LastPass or practically anyone else to be 100% secure. I use keypass, and store the file somewhere I can access remotely (online file storage) then can access it via my phone. If someone hacks your file storage account, they still can't access your passwords. The master password can be as complex or composite as possible and you never enter it into anything except the secure screen in keypass. There are some neat plugins for keypass too.
TL;DR keepass can do everything lastpass does, while you still hold all the keys and the data.
TL;DR keepass can do everything lastpass does, while you still hold all the keys and the data.