you may be able to set up your own local DNS server to handle just that request and any other request would fall through to the next DNS server you list. this would only work for the local network[s] served by the local DNS. what i recall is that there were many requests to fix this over 5 or 6 years and one day google just closed the issue marking it "won't fix (obsolete)" which makes no sense but when you're google it does not have to make sense. case in point is most recent google project tango. alternatively, you may be able to use a "hosts" file on android device but then that file would need to, if it worked, be on any device that needed access.
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.
As i know the omega has a firewall active ... so 8080 is might not open for the modem network. And not forget to check the modem for port forwarding of 8080 (you have to access as xxx.xxx.xxx.xxx:8080).
Maybe have a look in the wiki about the router/wireless extender tutorial for the omega, to see how to configure the firewall from it.