Masa0301,
Please state what exactly do you like to know about what do we know of current limit operation on the LP5907 LDO? In a nut shell the device will NOT allow its output current to exceed 500mA typical, that is like shorting Vout to ground which is specified by the Isc parameter in the DS. The internal circuit will clamp it to the stated limit.
Thermal to Vout data is not meaningful without qualifying the loading condition. You can easily and best perform it your self in your application board (because you thermal heat sink capability in your actual case can make a big difference) by sweeping the Vin and changing to various loading conditions while monitoring the temperature of the package either via a thermal couple attached on the chip top, or using a IR temp sensor gun (similar to those use to take one's temperature in the ear). I don't believe you can change the Vout of the regulator yourself. Not even sure why you might wish to gather "thermal vs Vout voltage"? Hope this helps.
Kern