Though seasonal AF/KL, Ibiza airport does have a lounge - see below for additional information:

Name of the lounge: VIP Cap Des Falco

Location: after security, make a U-turn to your right, it'll be in front of you

Opening Hours: 06:00-23:30, Monday-Sunday

Entry requirements: Regular Skyteam requirement. If you're not flying in Business, you might be required to display your FF card (an actual card or from the app)

Food offer: Warm and Cold, Fruits, Cereals, Cheese, Snacks

Drinks offer: Non-alcoholic & alcoholic (Wine, Beer)

Services
Wifi: YES
Showers: NO
Toilets: YES
Quiet zone: NO
Loungers/sleep area: NO
Business area: NO
Spa: NO
TV area: YES
Passengers are called: NO
Information screen: YES
Newspapers: POSSIBLE (visited during Covid)

Other information
Number of seats: 40
Level of noise: Low at time of COVID (could be higher with more guests)
Design: Modern, very comfy chairs
View: YES
Multi floors: NO
Terrace: NO
Smoking area: NO
Direct boarding: NO