A player does not need to have a minion on House of Nine Lives in order to use the base's ability.
General rule of thumb: If you've already read the instructions - especially the definitions of terms - then you know all the limitations on cards from their text. Of course, there are some complicated cards, but there are no additional restrictions in the game. I often get asked whether "all minions" is limited to a base or a player, etc. If there is no limitation on the card, then there is no limitation.