Hi,

I want to boot RT-Linux (RTOS) on MiSoC. Does it Supports?

Thanks :-)

Probably doable, some people are running full Linux on Vexriscv.
Unless you are building some kind of OpenWrt router, embedded Linux is usually bloated and ultimately pointless though.

I want to RT-Linux for real time application. MiSoC has LatticeMico32 CPU. I am not sure weather it supporting or not.

You can select VexRiscv in MiSoC. Probably better supported.