I'm reading Francois Recanati's "Unarticulated Constituents" and his discussion of the verb "eats" has gotten me thinking. "Eats" can occur both transitively and intransitively. When "eats" occurs transitively, we can represent its extension by eats2 - the set of all ordered pairs of eaters and the food they are eating. When "eats" occurs intransitively, however, Recanati suggests that we represent its extension by eats1 - the set of all eaters. The basis for his suggestion is that context need not provide a particular food that the speaker wishes to state that, e.g., Tim is eating when she utters "Tim eats".
I have my worries about the effectiveness of this case in support of Recanati's larger argument, but I'll assume the analysis for now. The situation is that intransitive "eats" refers to eats1 (or the property whose extension is eats1) and transitive "eats" refers to eats2 (or the relation whose extension is eats2). Is "eats" (lexically) ambiguous? In favor of an ambiguity, note that "eats" can refer to two different relations, and (or which) can have two extensions with fundamentally different structures - one is a class of individuals, the other a class of ordered pairs. The sentence "Eat!" seems to be ambiguous between the two readings, but it is hard to say that this ambiguity is structural - the sentence has no (surface) structure to speak of.
On the other hand, I think we can fix the reference of "eats" generally by a simple rule - if "eats" is intransitive, it refers to (the property whose extension is) eats1, and if "eats" is transitive, it refers to (the property whose extension is) eats2. Notably, sentences with "eats" are ambiguous between an assignment of eats1 or eats2 to "eats" whenever they are structurally ambiguous between a transitive and an intransitive reading.*
I suppose we can say there are two types of lexical ambiguity - referential ambiguity and semantic ambiguity. "Eats" is referentially ambiguous because it can refer to two sets, which are structurally quite different. It might not be semantically ambiguous because there is one simple rule that either fixes the reference of "eats" in a context, or gives the meaning of "eats" - the word has one reference-fixer, or one meaning.
* - Consider:
(1) If he eats an apple a dollar.
We can imagine a situation in which (1) is ambiguous between "If he eats an apple, it will cost a dollar" and "If he eats, it will cost an apple a dollar". (I have deliberately removed the punctuation, which would give away the intended reading.) Similarly with "Eat!" above. In these cases, any ambiguity in assigning eats1 or eats2 to "eats" can be chalked up to the structural ambiguity in the sentence.