I don't have an LG, but have had an external LaCie burner for years. First, there shouldn't be any need for software unless you want to add some burn software (such as Roxio Toast); I use either iDVD (for movies), iTunes (for music), or Toast (for either). You can also use iPhoto (I don't use it so I don't know all its capabilities).
In any case, my burner does not show up on the desktop. However, once I insert a DVD, that icon will show up - that means your Mac knows the burner is available. You have to set the CD & DVD preference pane (System Preferences) to show them on the desktop.
So what kinds of files do you want to burn? If it's just data, follow den.thed's advice - if your DVD is showing on the desktop and it's just files/folders, you should be able to drag those onto the icon as well (or use the burn folder) and burn using Finder and/or Disk Utility. Movies, slideshows - videos of any kind - need encoding/burn software (such as iDVD, iTunes, Toast).