Tente isso. De um terminal:
$ mkdir -p ~/.local/share/applications/
$ echo "[Desktop Entry]
Version=1.0
Name=Luakit Web Browser
Comment=Browse the World Wide Web
GenericName=Web Browser
Keywords=Internet;WWW;Browser;Web;Explorer
Exec=luakit %u
Terminal=false
X-MultipleArgs=false
Type=Application
Icon=luakit
Categories=GNOME;GTK;Network;WebBrowser;
MimeType=text/html;text/xml;application/xhtml+xml;application/xml;application/rss+xml;application/rdf+xml;image/gif;image/jpeg;image/png;x-scheme-handler/http;x-scheme-handler/https;x-scheme-handler/ftp;x-scheme-handler/chrome;video/webm;application/x-xpinstall;
StartupNotify=true
Actions=NewWindow;" > ~/.local/share/applications/luakit.desktop
$ update-desktop-database ~/.local/share/applications/
Em seguida, em Configurações do sistema > Detalhes > Aplicativos padrão, você deve poder selecionar Luakit Web Browser
.