The good news is, LCS only requires firmware version 2.0. With 2.0, you still have the option to downgrade to 1.5 and run homebrew. Homebrew is not just about cheesy games and emulators; any kind of mods or trainers or cheat device type codes will only be possible if you can run homebrew.
A copy of the 2.0 upgrade is included right on the GTA:LCS disc, here:

There's no need to go to Sony and download an upgrade, and you shouldn't anyway because they'll stick you with 2.7. If you upgrade to 2.01 or higher, there's no way to downgrade.
Update:
I got in through the savefile. CheatDevice works with 2.0, 2.01, 2.5 and 2.6 but will NOT work with 2.7.
Firmware 2.7 patches the GTA savefile exploit. Do not upgrade to 2.7 or you will lose all ability to run homebrew or the CheatDevice.