If sqlite package (or, for example, sqlite-libs package) was accidentally removed from your system, you can't reinstall it using dnf or yum because they depend on it.
To fix this problem, download missing rpm package from
https://admin.fedoraproject.org/pkgdb/package/rpms/sqlite/.
From the downloaded file location, run command:
rpm2cpio sqlite-libs-3.11.0-3.fc23.x86_64.rpm | cpio -idmv
It will create
usr folder with extracted files. Run next command to copy them to the right location:
Pay attention to the package architecture.
You should be able to use dnf again. It would be good to reinstall missed package with dnf again:
sudo dnf --best --allowerasing install sqlite-libs