You can pass under the top part of a limen or over the bottom part but you can't pass under a threshold.

You can specify limen superum 'lintel' or limen inferum 'sill, threshold' (literally, upper and lower threshold), but I see what you mean. Latin limen is not a good translation of the English scientific metaphorical notion of 'threshold', just the door jamb bits.

It's like saying that 'feet' is a good translation of a word meaning 'hands and feet.'

So, you're saying that 'finger' is not a good translation of Latin digitus, because that word can also mean 'toes', and even 'inch'? I often thought that translation is impassable.

Ceci n'est pas un seing.