When LCD's came out there was a warning about the lifespan of the item of about 5 years before they were needing replaced. Well that myth can be dispelled. I have a BMW motorcycle which is 27 years old, it has a LCD readout for the clock and gear position indicator and they both work as they should. I have a pocket calculator which is about 3 years older than the bike and that works too (including the photocell which powers it).
I now think that the warning about the life of LCD's was greatly underestimated because on most instruments that use them they are not operating all the time. Both of my items above are not switched on all the time and nor will the LCD of the Nikon so the life will probably be in decades not just 5 years.
I have only heard of one brand/model of camera which has regular LCD problems and this was the Minolta 9000. They were very well built but you only very very rarely see one for sale now in any sort of condition because the LCD was it's Achilles heel. The 7000 model which was brought out a year or so before never had the same LCD problem. Your F3 has many years left.