Is it possible to lucid dream without having to be tired to fall asleep? Could you just at any time of the day regardless of being tired or not… close your eyes and try to encourage a lucid dream or would that be just meditation which is a whole different story?
Unless you have tranquilizer darts on hand or have extreme meditation skills i dont think its possible. If you are not tired you will lay awake until you are.
Its quite simple actually. Unless you fall asleep, you won’t have dreams (not counting visions in medition etc). So, if you want to LD, you need to sleep, wether tired or not.
Hey Meltedbutter! Welcome to LD4all 
Do you mean something like extremely vivid daydreaming? Imo this is really difficult to achieve. But fact is that if you have a short nap in the afternoon, tired or not, you’ll have much more chance of becoming lucid than during a regular night.
It’s hard to get to sleep when you are not tired.