This paper leverages past sentence processing studies to investigate whether monolingual and multilingual LLMs show human-like preferences when presented with examples of relative clause attachment ambiguities in Italian and English. Furthermore, we test whether these preferences can be modulated by lexical factors (the type of verb/noun in the matrix clause) which have been shown to be tied to subtle constraints on syntactic and semantic relations. Our results overall showcase how LLM behavior varies interestingly across models, but also general failings of these models in correctly capturing human-like preferences. In light of these results, we argue that RC attachment is the ideal benchmark for cross-linguistic investigations of LLMs' linguistic knowledge and biases.