It turns out that in the Ultimate Talkie Edition of Monkey Island 2: LeChuck’s Revenge, touching the model lighthouse in Phatt Island but not retrieving its lens creates a softlock condition. When returning to Scabb Island, Dredd leaves to go “do errands” and consequently makes you stuck without the ability to get the map reassembled. The cartographer in Scabb needs that lens but you have no boat to go back!

This bug does not exist in the non-Talkie versions as far as I can tell. I did some searching in various places and it appears that I am not the first person to run across it.