I have a Mac with WiFi connected to a router, internet works just fine there. I also have a PC with Linux Mint, and no wireless network card, so I connected them with a cable one to the other. Have enabled internet sharing at the Mac. I have also run
sudo sysctl -w net.inet.ip.forwarding=1 and
sudo sysctl -w net.link.ether.inet.proxyall=1
Now they have their own LAN - from the Linux machine I can connect to the default gateway (192.168.3.1) and I see a webpage I setup on the mac which only displays "It works". But when I try to connect from the Linux machine to somewhere else I don't get a respond. For example when I try to get to the router at 126.96.36.199 the Linux fails, and the Mac displays the routers login page. Notice, they are on different LANs, since the network-mask is 255.255.255.0 (for both).
I don't really care if at the end they'll be connected at the same LAN or not. I just want the Linux machine to have internet access.