I tried to just add the ids of the new chips, but that isn't enough, it doesn't work. Part identification works OK, but loading data to RAM fails, which is a necessary step for flashing.
Also, since I didn't get any reply from NXP w.r.t. duplicate ids (see this question: https://community.nxp.com/thread/459176) I didn't yet push the change to github.
My version at GitHub - starblue/lpc21isp now supports LPC84x, LPC80x and LPC83x (the latter untested).
The issue was that ISP on LPC84x and LPC80x uses more RAM than LPC81x and LPC82x, so ISP conflicted with the RAM buffer for flashing. After moving the RAM buffer it works.