Welcome to FT!
To build on what the prior poster said, some lounge arrangements including Lufthansa, Delta and starting in 2023 (for folks spending less than $75K), the Amex Centurion Lounges only allow access for the cardholder. While the latter two allow for purchased guest access, LH does not.
What most of us do to get around this is we add our spouses/close family as Authorized users. This way they have a card they can use to get access both with and without the primary cardholder. It's (I think) $175 but covers up to 3 additional people.