well first off your going to need a copy of the unpatched gta:lcs with the 2.00 ver update on it. Your probably wondering why...well it has an exploit inside it that allows you to be able to downgrade to 1.50. Anyways if you do not own a copy you can check your local movie/video game store to see if they have a copy available to rent.
Anyways since you have 2.81 your going to have to upgrade to 3.03 since there was no downgrader released for 2.81 itself. you can find all the files and instructions for this process in this 3.03 downgrader tutorial.
HERE
Once you have successfully downgraded your going to want to upgrade to any of the custom firmwares. I'll send you a link to the easy installer for 3.03 oe-c. This is what i prefer but thats just me, if you prefer a diff custom firmware just let us know and i'm sure one of us will get back to you with a tutorial or an easy installer for that firmware. Anyways...
HERE
For future reference we have a foprum dedicated strictly for tutorials. There is a master guide inside there that has about 20 in depth guides for the majority of your standard psp needs.
Here you go