Created attachment 389000 [details] screenshot showing the Network Configurator has no icon In lxpanel there is no icon for Network Configurator.
I think the root cause is outside the dhcpcd realm. On my lxpanel (although NetBSD, not Gentoo) there are icons for each menu item, and you're missing a lot of basic ones. Maybe lxpanel is missing a picture decoding type somehow? Easy test - ensure that dhcpcd.png and/or dhcpcd.svg exists in the installed files in the correct hicolor icon locations.
Indeed it seems you are missing some sort of icon support in your LXDE. Perhaps one of the basic icon themes? I don't think this is a package specific bug either.
Just copy dhcpcd-ui.desktop to your home direcotory (`~/.local/share/applications' to be precise.) And then edit the icon entry to what you like (`network-server' or the likes will do.) This bug can be marked as SOLVED|WON'T FIX. (I'm not going further than that.)