This was taken from the vivaldi forums. It explains how to install the LastPass extension into the vivaldi browser and should work for other plugins as well (although I haven't tried yet).

The Procedure

Install the Chrome extension source viewer (CRX Viewer) in Chrome
Go to the Chrome Web Store and search for the LastPass extension
Right click on the LastPass search result to bring up the context menu
In the context menu selecte View extension source
In the page that opens, click on the Download link in the upper corner
Go to the Downloads folder and make a new folder (e.g. mkdir lastpass)
Move the zip-file that you downloaded into the folder (mine was called hdokiejnpimakedhajhdlcegeplioahd.zip so I assume the names are random)
Unzip the download
Re-name _metadata to metadata (the post suggests deleting it, so that might work too)
In Vivaldi, open the link vivaldi://chrome/extensions
Click the Developer mode checkbox
Click on Load unpacked extension
Select the folder you unpacked the zip file into (lastpass in this case)
Configure Last Pass

Conclusion

This gives the procedure for installing extensions like LastPass into the Vivaldi browser. In the course of writing this up I found out that you don't need to do this for all the extensions (just the ones with leading underscores in some of their folder names, I think). For other extensions just install them from the store - they seem to work out of the box.