The question is going to be a difficult one for people here to adequately answer, because Chamberlin's book is drawing on a debate that is not incredibly pertinent outside of a medieval context, and also concerns a text (Piers Plowman) that is not widely read by people other than medievalists. One resource you might consider is looking at some reviews of the book, which will help you contextualize it and which can generally pretty easily found through google or searches in university library catalogs.

The basic thing you need to understand is that for many medieval authors, things like puns were of huge importance, which can be a bit hard to conceive of today. For most people, puns are either groan-inducing humor of the lowest possible variety, or puerile jokes about sexual innuendo. But for medievals, puns were of great importance, and it was widely believed that they could reveal important truths about the world.

Thus, in one classic story from Anglo-Saxon England, Gregory the Great sees an Anglian slave-boy in the market and arrives at the decision to send missionaries to England as a result of a series of puns. What race is this boy? He is of the Angli. No, says Gregory, he is not of the Angli but the Angeli (angels) because he is so beautiful. What kingdom is he from? Why, from Deira. Ah! He has been sent to us that his people may be saved de ira (from the wrath) of God. Who is the king of this land? Aelle. Aelle, you say? Alleluia! For we shall send missionaries to this land. As a paraphrase, I'm playing somewhat fast and loose, but it's exactly those puns, and it's an important story that gets told across several centuries. And medieval culture is full of these kinds of things, from Isidore's Etymologies on down. These puns (sometimes fancily called paronomasia), are everywhere, and they were seen as revealing important religious, philosophical, and historical truths.

This is an example of what Chamberlin is after when he talks about lexical ambiguity. It's the ability of words to have multiple linguistic meanings at once, and if you want to read a study on more modern things, you might read Empson's classic Seven Types of Ambiguity. Lexical ambiguity is a pretty broad category, that could include puns, homophones, metaphor, and a number of other things.

The idea of the ambiguity of words as words is after something a bit different. You give the example here of onomatopoeia, which makes a certain amount of sense. The word pop is at once both the lexical item and the sound that we encounter. (Slight tangent: Modern stylisticians, for that matter, even distinguish between lexical and non-lexical onomatopoeia. In teaching this, I ask students to each transcribe me making the sound of blowing raspberries, and invariably every student differs, at least a little, in the way that they transcribe the sound.) In any event, something like pop is both a word and something not a word all at once, although this is really an example that is more meant to be a bridge to understanding than an important example in Piers Plowman.

What Chamberlin is really after is the fact that medievals had much broader classes of words that that fall into this category. Some of this is due to the nature of allegory itself, a genre that is not terribly popular today, but that is all about blurring the line between words and their referents. Words like Truth have a meaning as a word but also meaning as important allegorical figures within Piers.

But even apart from strictly allegorical treatments of specific words, medieval authors saw words as reflective of reality in ways that are quite foreign to us today. Etymologies frequently lacked what we would think of as factual truth, and were made up based on real world connections between things that sometimes had nothing to do with each other. Etymologies constructed in this way often rely on words that have similar sound (a kind of lexical ambiguity) but also draw direct connections between real world things and the words used to describe them, suggesting a certain ambiguity of the words as words.

What Chamberlin is after, I think, is demonstrating these two types of ambiguity as importantly functioning together in Piers Plowman in ways that are not clear to us because of how we think about language. We tend to follow Saussure in thinking about language in terms of signifier (the word "apple") and signified (the actual apple), and recognize that the two are related to each other in a completely arbitrary way. Except in rare instances, like onomatopoeia, we don't think that the form of the word has anything to do with the thing that it describes. We have the benefit of having much more accurate etymologies today than those created by Isidore or drawn on by later medieval authors, but having more accurate etymologies isn't really an advantage in analyzing literature constructed by people who believe that etymologies reveal ontological truths about words.

I hope that helped some. Some of it is likely inaccurate to Chamberlin's argument, since my understanding of it came from quickly skimming what was available in Google books. Book reviews will probably help a lot, unless you can find someone who has recently read the whole book.