You can use something like installease or casper composer to make a package from a Logic install.
Installease is free, more info on how it works and download from here Package Building: Absolute Manage - Automated Client Management for Mac and Windows Computers and Software
Casper Composer isn't free, details here
JAMF Software: Products - Composer
Both apps are part of larger suites, that allow management of OS X clients, software updates, licence management that kind of thing.
The installer you create can then be deployed using Apple Remote Desktop or deploystudio.