Hi Ramon
To clock the KL03 LPUART from the XTAL you need to set
SIM_SOPT2 |= (SIM_SOPT2_UART0SRC_OSCERCLK);
so that the OSCERCLK is connected to it.
Before that, you also need to enable the oscillator:
OSC0_CR = (OSC_CR_ERCLKEN | OSC_CR_EREFSTEN); // enable the oscillator and allow it to continue oscillating in stop mode
The crystal will need to have a frequency that is suitable for the Baud rate generation - eg, the 32kHz on the FRDM-KL03Z is not because it is too slow.
Regards
Mark
http://www.utasker.com/kinetis/FRDM-KL03Z.html