Hi, James,
You are right, the LPC802 does not have DMA module. I have checked the Fig 21 USART block diagram, the so-called "Transmit DMA request" and "Receive DMA request" are typo, I will tell the documentation to modify the doc UM1105.
Thank you for pointing out the typo.
Hope it can help you
BR
Xiangjun Rong