How to power an arduino controlled string of RGB LED's from separate power source
Simply power the LED driver (i.e., its VCC pin) with a battery (or other higher-current-capable source), since the Arduino pins are only capable of sourcing 50 mA.


First of all, you won't even need a transistor, if you use a battery as I mentioned above. But to answer your question, if you were using a transistor: while there is lag, lag won't be significant enough to affect your application here.
And secondly, the TLC5940 is a constant-current driver, so you're fine. A constant current source/sink is exactly that -- it ensures a constant current flows independent of power supply fluctuations/other conditions. Thus your LEDs will light up with constant brightness.


Finally, a clarification regarding PWM with the TLC5940: You don't use PWM of the Arduino pin to directly create PWM on the TLC5940 I/O pins; that's NOT how it works. Instead, the TLC5940 uses serial communication with Arduino -- so you would send it instructions from the Arduino (via SPI or bit-banging, for example; see this TLC5940 Arduino library), and the TLC5940 reads those instructions and performs PWM on the desired I/O pins as instructed.