I’ve made it. Initially I gave up and decided to install Windows (sic!) on that server. On a second thought I gave Open Manage Essentials a last try. And it worked. 
I have a couple of identical R710 with iDrac enterprise. Both have VMware ESXi 6 with OMSA agent installed. Recently I have decided to upgrade all old firmware on both servers. Following this guide I have made a bootable CD and run it several times on both servers. Then I have compared results via iDrac. First server seemed to successfully receive all the updates. Second one seem to stuck with old Bios(6.3), iDrac(1.92 Build 05)  and PERC H700 (12.10.4-0001) firmware. I understand that I have somehow to try applying older versions of firmware first. What would be the best sequence to do that? Can this be done via lifecycle controller (servers do not have internet access)? Or should I build a bootable FreeDos media?
Problems upgrading fw on R710