I think any theory on the market can probably handle such sentences. The first part of the analysis is simple relativization, where a noun in a higher clause also has a role in a lower clause, for example "I saw the man who drank the coffee", where "the man" is both the object of seeing and the subject of drinking. As a special case, you can arrange your choice of subject and object roles so that the higher subject is also the lower object, and the higher object is the lower subject (the David-hating-lizards example); or other permutations as you consider. The second part is that a would-be postnominal modifiers precede the noun subject to conditions worthy of separate discussion, so that "The man who is singing" becomes "The singing man", and "The man who is singing bawdy songs" becomes "The bawdy song singing man". You get "David hates David-hating lizards relativization and preposing.
The third example doesn't work, which makes it interesting. To make it clearer, we should change the verbs, to wit: David loves lizards. Lizards bite blondes. Blondes hate David. You might think this would yield "David loves David-hating blonde-biting lizards". The problem is that this doesn't preserve the semantics of the simpler parts, since in this merged version, lizards bite blondes and hate David, whereas we want something where it's the blondes who hate David. Lizards can bite David-hating blondes and David can love blonde-biting lizards, and that's the end of it.
There is a limit on relative clause reduction and preposing -- it can't be just any relative clause. Note that you can't say
*"I know the bought a house man", meaning "I know the man who bought a house". To be preposable, the clause has to be reducible to a compound (normatively, you should stick in hyphens, which reflect the different intonational structure of preposed clauses). Nouns have to be singular ("book-buying child" but not
*"books-buying child") and the verb has to be a participial form, not a tense-inflected form ("man-eating tiger" or "moth-eaten pants" but not
*"moth-ate pants"). You can have one VP thing in the clause ("slow-moving car", "very slow-moving car"; "house-buying business", "dilapidated house-buying business"), but not a verb-plus particle and an object (
*"answer up-looking student" or anything like that) and not some string of postverbal modifiers (
*"book to Sally giving student" etc.). So, while you can merge three clauses into "David loves lizards which bite blondes that hate David", you can't do that plus compounding of all of the clauses.
Rules for forming relative clauses are not all the same and are highly variable across languages. See Keenan & Comrie 1977 Noun Phrase Accessibility and Universal Grammar for discussion.