Off the top of my head, I cannot think of any medications that need to be taken on an empty stomach, but if you want to be fanatical about it then the time lapse is about an hour and a half,although this gives a chance of forgetting your medication, which is far worse than the timing.
as for thyroxine.....it doesn't matter......take it at the same time every day. morning is the usual time but now there seems to be murmurings in some medical quarters about taking thyroxine before bedtime.
I pay little attention to these "murmurings"
Routine, some tablets, same time every day.....is the watchword.