I am not sure what you mean by 'integrate'. Perhaps the following beginner-level brief will help.
***
LabStoRe is a web-based application. The application logic and code for display are handled by a web-server. The display itself and the user interaction occurs on a web-browser. Three things are therefore needed to use LabStoRe:
1. A web-server application like Apache and IIS. You can download and install Apache for free on your computer. Check the internet on how to do so.
2. PHP, which you have. The web-server application needs modules to interact with the PHP. Check the internet for more on PHP-enabling your web-server.
3. The MySQL database application, which you have as well.
Using LabStoRe involves clicking on links, filling forms, etc., on web-pages. Such actions are transmitted by the browser to the web-server. The server in turn passes them to PHP. PHP with help of MySQL then manipulates information, sending any required information back to the web-server, which in turn passes it on to the browser.
A web-site is of course needed for the internet browser to connect to. If such a web-site is accessible over the internet, you'd use that internet address to go to LabStoRe. If it is just on your computer and not remotely accessible, using the browser on the same computer you'd use a 'localhost' address.
The web-site files will be the LabStoRe files you downloaded and un-zipped.
The MySQL database server application will hold and provide the PHP application interactivity with a database that holds the LabStoRe data.
With a web-server and a web-site available, installing LaStoRe thus involves the following:
1. Putting the downloaded files in the right folders.
2. Creating a MySQL database and populating it with some initial data (using the .sql file that is in the zip file).
3. Editing the config.php (in the zip file) to customize your LabStoRe set-up.
More information is in the readme file in the zip download.