First of all, I don't know if anyone else has had this problem or not on LXLE, but after a recent update, every time I logged in, I found TWO network icons in the LXDE panel. While it didn't cause any problems, it was very annoying. I tried several things to fix it, to no avail. But then, while searching for a solution to this problem, I found something that sounded like it would do the trick, adapted it to LXDE, tried it, and it works perfectly! Here's how I did it:
Open PCManFM to your home folder.
If you don't already have your hidden files and folders displayed (that is, files or folders whose names start with a dot), click "View --> Show Hidden" (or press Ctrl-H) to make them appear.
Navigate to /home/yourusername/config/autostart. (where "yourusername", of course, is your login name).
In that folder, you should see an icon labeled "Network". Right-click on it and, in the popup menu that appears, click "Properties".
In the dialog box that appears, click the "Desktop Entry" tab.
In the "Command:" field, insert a "#" as the first character, which will comment out the command and stop it from executing.
Log out and back in, and you should find that you network icon appears only ONCE in the panel, like it's supposed to.