Perhaps the .lan is being resolved for clients by the Omega2's DNS server, and therefore only works on machines that are clients of its wifi AP such that these machines would be passing their lookups through the Omega.
Conversely the .local names utilize mDNS, for which a computer must cooperate. Mac's, iPhones, and most Linux boxes do this by default. Windows doesn't without an install of something like Bonjour, and the Android browser doesn't (though other Android apps can be written to).
Or you can use the IP address - but your router might re-assign that at some point and surprise you - it can be the same for weeks and then just when you think you have it memorized and stop checking, they can all get reshuffled.