Supposed you have subversion installed on your system:
Open Terminal where you want to have your Lazarus components and just issue this command
svn checkout svn://svn.code.sf.net/p/zeoslib/code-0/trunk ./ZeosLib_svn
Now there will be a new folder in current directory with name ZeosLib_svn
Uninstall sqlite component if present in your lazarus, delete existing folder of this existing component.
Go to folder ZeosLib_svn and open and "install"
/ZeosLib_svn/packages/lazarus/zcomponentdesign.lpk
Put component ZConnection to your form and inside this connection select protocol sqlite. Thats all to get you started
Further information can be found at:
https://zeoslib.sourceforge.io/
and
https://sqlite.org/forum/forum
See also? sample app. at
https://drive.google.com/file/d/1Bvxr5A3XQkg2V3wdpLP20OY-FsbbOWWM/view?usp=sharing
Sqlite is strange if you are used to Oracle ... Databases
Good luck
John