I have a dropdown (list) type question, and I want to conditionally hide some answers from the dropdown, based on a response to a previous question.

I can do this using multiple choice, because there is a relevance equation option for those answers -- but not in List type.

Any advice on how I can handle this?

You can't.

Unfortunately there are two concepts in Limesurvey:

1. Answer options, they do not have relevance equations (for example the items of a dropdown list)
2. Sub questions, they do have subquestion relevance (e.g. Array questions, multiple choice, etc.)

You are not the only one that is missing answer option relevance.