I have a 'Majestic' UFO omni-antenna on the top of my 17m mast
It worked fine with the original analog only Majestic 17inch LCD. I upgraded to a 22 inch Teac LCD with built in digital tuner and it is now FANTASTIC!
Replace your old analog LCD with a new digital one and you'll be fine. Don't even think about adding a set-top box to your analog TV as it just adds complexity and is yet another box to suck power.
(Hint... make sure that the LCD TV has a 12V input... don't need an inverter