I’ve built my website with Beaver Builder Plugin (lite version). Now I want to upgrade to the standard version. Is this possible for an active website?
Yes, that should not be a problem. Make a backup first (always 
). Then remove the lite version and upload the standard version. As far as I know it’s a different plugin. All your content should still be ok. If you want to be extra secure, test it on a staging site first. But if something goes wrong you should always at least be able to go back to the lite version.