Answer
Neither — lobbies are configurations, and translation scanning for lobby elements/pages defaults to (and should stay on) the 'CONFIG' component rather than 'No Module' or a purpose-built new module; there's no need to create a separate module just for this. Once translations are saved against CONFIG, they're stored in the same ordinary translation tables used for the rest of Enterprise Explorer, so the standard Translation Manager tool (Administration > Export/Import Language Files, selecting the CONFIG component under Foundation1 and the layer/languages needed) can export and import them the same way it does for any other translatable content, including moving them between environments.