OK which CMS you have? Does it support SQLite? Do you want people to download the database or import new data only? Or to put it in an other light does the database contain user data as well as your data that you want to preserve or a simple replace with the new database is acceptable? Does you server support cgi applications? Notice I did not ask for cgi scripts because since php is a scripting language and the interpreter is a cgi application every one assume that php is a cgi script. So can you upload a cgi application on your server and call it through some url? If yes try to write a simple cgi application in lazarus that will return a string to the browser and see how that works.
Then you can decide if you wish to use mormot, brook or some otehre framework to speed up your development or you want to stick with simple cgi scripts and sqldb to export/import data.
Please note the complete absence of reference to what OS bitness the server requires, that is because for those first steps you find and install a webserver in your computer preferably the same weeb server your site uses (apache most probably) set it up to support cgi application and experiment there with your cgi and return string before targeting your web server.