Here is the sample .desktop file that You can modify and use to launch any AppImage single click from Linux menu (sometimes called Kickoff menu, or start menu) or right click the item to call its menu that will have appimage update option so it will update appimage and then run it.

Code:
[Desktop Action NewShortcut]
Exec=/bin/bash -c '/usr/bin/wget -NcqO $HOME/apps/LosslessCut-linux.AppImage https://github.com/mifi/lossless-cut/releases/latest/download/LosslessCut-linux.AppImage'
Name=Update only

[Desktop Action SubMenu3]
Exec=/bin/bash -c '/usr/bin/wget -NcqO $HOME/apps/LosslessCut-linux.AppImage https://github.com/mifi/lossless-cut/releases/latest/download/LosslessCut-linux.AppImage';/bin/bash -c '~/apps/LosslessCut-linux.AppImage'
Name=Update local file if is older/diff.size than latest version & Run it

[Desktop Entry]
Actions=NewShortcut;SubMenu1;SubMenu2;SubMenu3;
Categories=AudioVideo;
Comment=GUI tool for lossless trimming/cutting of media files
Exec=~/apps/LosslessCut-linux.AppImage
Icon=~/apps/LosslessCut-linux.AppImage
Name=LosslessCut - run or update
NoDisplay=false
Path[$e]=
StartupNotify=false
Terminal=0
TerminalOptions=
Type=Application
Version=1.1
X-KDE-SubstituteUID=false
X-KDE-Username=
Things you will need to update:
1) apps/LosslessCut-linux.AppImage
2) https://github.com/mifi/lossless-cut/releases/latest/download/LosslessCut-linux.AppImage

This .desktop file i have in /home/$(whoami)/.local/share/applications/

Feedback and improvements are welcome.