"lao" means "old" as in "old age" or "time"
i.e. 老朋友 compared to 新朋友.
老朋友= old friends, while 新朋友 means "new friends".
旧 translates to "old/worn out" and is only used with non-living things.
e.g.旧衬衫 - an old blouse
This is probably the general difference. There may be more to it, but I did my best to explain it.