Rockstar have just sent me a little application that you can install on your PSP to enable the custom soundtrack option on Liberty City Stories, the download is just under 1MB and please read the readme that comes in the zip file for full instructions on what to do.
Judging by reactions on various message boards on the interweb, this isn't what fans wanted at all, granted, it's better than nothing, but there are a few major drawbacks to this app.
First and foremost, you can only convert tracks from original audio CD's, so you can't go downloading music from iTunes, or copying your friends' discs, you need the real thing.
Secondly, you can only use these tracks on LCS, they can't be used elsewhere on your PSP.
Thirdly, the program only works on Windows computers, so around 15% of the population have no such facility available.
Fourthly, you choose custom tracks OR radio, not both, you'll need to go back into the options again if you want to switch between the two.
With reports also flying around that Rockstar are allegedly deliberately delaying LCS in Europe to rain on Nintendo's Gameboy Micro parade and Microsoft's Xbox360 release. It's not looking great for consumers as they have to wait even longer for the game.
However, having said all that I'll point you in the direction of the application for those who do want it - Download GTALCS Custom Tracks Loader