Crystal oscillator circuit
You can use XTAL2 as your ADC's clock source, but you may need a buffer between XTAL2 and your ADC's CLK pin, such as a Schmitt-trigger 74HC1G14.



Update:

As the OP's question in comment:


  Why 74HC1G14 is needed?


Per LPC2183's datasheet, XTAL2's output voltage ranges from -0.5V to 1.95V. This voltage level may not high enough to drive your ADC's CLK input. And this may also slow down the edge rate of the clock signal.