If it is "secure" depends on your analysis. Lockwise cloud storage appears to be secure.
The question of wether data should be protected against other programs is something that is comes up in the media and discussions quite frequently.
There are main schools of thought:
- One, often levelled by third parties, is that access should be as hard as possible. Thus data should be locally encrypted and locked down as much as it can.
- The other that there is no defence against an attacker who has access to your account anyway. Therefore it doesn't make sense to expend much effort against attacks by other programs running within your account.
Major browser vendors mostly go with the latter. Presumambly also with the idea that if you make password management easier, then more people will use it - and this will be a greater security benefit overall.
Third-party password managers will often take additional measures to protect the local data, at the cost of additional hassle for the end user. Password management is always a tradeoff between convenience and security; and at the end of the day a using a reasonably secure password manager is much better than having a super-secure one and not using it.
For Lockwise, you can "secure" the local storage a bit by setting a master password.
None of the approaches is inherently "bad" though.