Similar problem was discussed here: Local DNS doesn't resolve router itself - #8 by vcunat
Myself, I managed to solve the problem on my Turris MOX just by adding router name (without .lan) and its IP into LuCI’s Network->Host names. At that moment, nslookup on the router started to resolve the router’s name. To get the same on my computer, I had to flush DNS cache. On my Ubuntu 18.04.6, it is performed by sudo systemd-resolve --flush-caches. Alternatively, you might restart the computer or wait long enough time for the cache to expire.