Thank you TheCoolest, it's the one I use, the only one that works for me on a Duemilanove.
The problem is now partally solved.
I have tried some libraries before posting here. Since then, I have found that some of them have very small differences.
This library http://playground.arduino.cc/uploads/Code/LiquidCrystal_I2C_85V1.zip
doesn't work in my case, but this one https://github.com/digistump/DigisparkArduinoIntegration/tree/master/libraries/DigisparkLCD
LiquidCrystal_I2C.cpp and ".h" files are slightly different.
Furthermore, the code that works is the following :
#include <TinyWireM.h> // original lib include
lcd.init(); // this is necessary
Malpartida's lib, seem to be much better. It has many advanced and interesting possibilities.
The problem is that it works with a Duemilanove and not an ATTiny, even with I2CIO.cpp modified to use TinyWireM.
That's why I tag this post as "partially solved".
I'm not satisfied with this, and I'm going to try to understand what's happening.
For that I need to debug or trace the lib, but I don't know how to do that. I've used the SoftwareSerial lib with the ATTiny, but don't know if it's possible to use it from inside lib classes.
If someone could point me to some method...