What are the origins of the Hebrew word pronounced "ed," meaning "witness?" It is spelled ayin daled. Is it related to the ayin daled portion of the word "Le-ad," which means "forever?" Does it also mean a contract and evidence? Is the origin Aramaic?
Gesenius's Hebrew and Chaldee Lexicon states that it is the present participle of a root ayin-waw-dalet, meaning 'return' or 'repeat', with an Arabic cognate `āda -- the idea apparently being that a witness is one who 'repeats' what he saw. It's presumably not an Aramaic borrowing, since it occurs already in Genesis. Gesenius lists the meaning 'testimony' in addition to 'witness'. In modern Hebrew, though, it only means 'witness'; 'testimony' is a related noun, edut.
As for whether it's related to `ad 'eternity', Gesenius thinks not: he derives the latter from a different root ayin-dalet-he. It seems conceivable that the two roots could be related further back, though; at least, one could certainly imagine a semantic relationship between 'return' and 'eternity'.
First, there's no need to insert a ל to עד "witness" to form לעד when עד on its own is already a homonym meaning "forever". The ל is a preposition that would yield something like "unto eternity".
Incidentally, another homonym is עד "filthy", derived from a root related to setting a period of time, seemingly connected to the menstrual cycle. I presume Biblical hermeneuticists aren't keen to hang all these meanings on the same peg.
So how do we determine which homonyms are polysemous, i.e. extensions of a single root? One way when we have roots of only two letters is to find the three-letter root that it comes from. (This is an assumption made when studying Hebrew that can be questioned, but no need to here.) Roots where we can't see the third consonant are "defective".
There are a few ways to "repair" a defective root, i.e. determine the third consonant. One is to look for a weak consonant that's likely to disappear: the vowel-like ו vav, ה heth, or י yod. One might come before, between, or after the two letters we can see, as in the common קום q-w-m "to rise". One set of reconstructions would thus be יעד y-ʕ-d or עיד ʕ-y-d or עדי ʕ-d-y.
There are also cases where a letter is commonly dropped from the beginning, e.g. the נ in נגד n-g-d "to tell" or the ל in לקח l-q-kh "to take", which are often missing in conjugations. But these cases are rare. And as I mentioned, looking for a lost ל at the start is pointless since the ל in לעד is a preposition, not part of the verbal root.
We can also look for a consonant that naturally assimilates into another. This typically happens with geminate roots, i.e. roots with two of the same consonant, such as רעע r-ʕ-ʕ "to do evil". That would let us reconstruct maybe עדד ʔ-d-d.
Once you have some candidates you go look for attestations in your dictionary or the text itself. In the text, you can find parallel conjugations. For example, we know that "middle-weak" roots are conjugated a certain way. Do we have any examples of a verbal עד that are conjugated like קום? Or we know that geminate verbs are conjugated another way. Do we have any examples of a verbal עד that are conjugated like רעע ? And so on. Also key is to compare related languages in which the "defective" consonant has not disappeared. Is there an Arabic, Aramaic, Assyrian, or Akkadian root, for example, that corresponds to a hypothetical עדי ?
Having found viable candidates, you then try to match up meanings to establish a reasonable semantic derivation, which is where some disagreement might come in. Sometimes it isn't a purely semantic argument but the vowels of the noun can also give hints as to root it came from.
Something like this has been done for many obscure words in the Bible, and to make a long story short, at least one source relates the different words spelled עד to the roots I noted at the start.