Umm, did you bother to check out the etymology of "reliable"? It doesn't come from the word "lie", but from the word "rely".

"Lie" comes from Old English lēogan, which meant pretty much the same thing it means today.

"Rely" comes from Latin religāre, which is the prefix re attached to the verb ligāre, which means "to bind" or "to link together".

The fact that a Germanic word and a Latin word happen to sound similar in Modern English does not mean that their meanings have anything to do with each other. "Lie" and "rely" have always been, and still are, very different words with very different meanings. "Reliable" has about as much to do with lies as the word "belief" has to do with bees and leaves.