Hi Soph6,
Please try install any other vsix file to make sure this problem is caused by the SQLite SDK or for all vsix files.
If all vsix have the same problem, the VSIX Installer may be broken. Please try to install vsix file through menu of Tools -> Extensions and Updates, then searching "SQLite SDK" under the Online node to install the extension that
you want to install. If also doesn't work, please try to repair your Visual Studio or re-install your Visual Studio to repair the VSIX installer.
If just the SQLite SDK has this problem, please check whether it supports Visual Studio 2015 Pro by unzip the .vsix file and have a look of the vsixmanifest see the InstallationTarget supports 14.0 or not. You also can provide the download link which
can let me try in my side.
If it is indeed caused by the SQLite SDK, I suggest you contact the author for this extension, who will check this problem.
Best Regards,
Weiwei