Can I only run uClinux/Linux on the LPC24xx/LPC3xxx boards?
No. Basically any RTOS will run on the boards. There are multiple ports to the LPC2xxx/LPC3xxx families, for example, FreeRTOS, Micrium, RTX (from Keil/ARM), embOS (from Segger), PowerPack (from IAR), and many more.
