Hi Veronika! I get similar brownish marks on my clivia leaves, but not at the crown/middle part..just on the outermost leaves touching the soil. I just leave mine alone, it does not hurt the plant. I also grow my plants indoors. Give it time, and continue to observe. If it does not seem to spread then maybe it is already healing itself.
If you think it is still spreading, then maybe it is time to visit the roots and check its conditions, maybe see if you can make your media a bit more grittier to help dry out the root area faster.
