I want to assign labels to various lists in one Trello board. For example, my trello board is one project; the lists inside the board represent various initiatives for the larger project; each of the initiatives relates to a particular strategic activity (use. share, build). So I'd like to label each list according to its strategic activity, but it seems only cards can be labeled.
That is correct; only cards can be labeled. You're not missing anything. Nor can you (currently) automatically assign colors to newly created cards in a given list, although you could always write something that took advantage of the Trello API to do what you want, if that makes sense for you.