I don't think this means anything at all. With so many thousands of words in the English language, and only twenty-six letters, it's no surprise that some letters will find themselves in similar formations.
How Do You Know It Doesn't Mean Anything?
If you think about it logically, the etymology of the words are completely different, and standardised spelling wasn't introduced until 1755, when Samuel Johnson published the dictionary. In Old English, the two words bear little resemblance to each other: evil was yfel and live was libban. They can both be traced back further than that, to a proto-Germanic 'parent' language, where they bear even less resemblance to one another.
Nobody sat down with a pencil and decided to make words from anagrams, and even if they had, it wouldn't make the words mean anything different. Besides, it's only in English that evil is live backwards; in French, they're mal and vivre respectively.
So many words spell other things when the order of the letters are reversed. It doesn't mean anything; drawer is reward backwards, and God is dog backwards, too. It's all just coincidence.