Direct proof of use
The F-35B Lightning II is directly documented in the 2014 War Against the Islamic State through official UK, Royal Navy, U.S. Marine Corps, and CJTF-OIR material from the 2021 HMS Queen Elizabeth carrier deployment. On June 22, 2021, the UK Ministry of Defence said F-35 jets from HMS Queen Elizabeth had carried out the ship's first combat missions against Daesh in support of Operation Shader and U.S. Operation Inherent Resolve.
U.S. Marine Corps reporting identified Marine Fighter Attack Squadron 211 aboard HMS Queen Elizabeth and said VMFA-211 began air operations in support of Operation Inherent Resolve on June 18, 2021. The same report stated that VMFA-211 and the UK's 617 Squadron flew F-35B Lightning II aircraft during counter-ISIS and protective overwatch missions.
Sources: Stealth jets fight Daesh in first combat missions from HMS Queen Elizabeth, U.S. Marine Corps Squadron Supports Operation Inherent Resolve from Royal Navy's HMS Queen Elizabeth
Narrative
The documented F-35B use occurred during Carrier Strike Group 21, HMS Queen Elizabeth's first operational deployment. The UK Ministry of Defence described 18 UK and U.S. F-35B jets aboard the carrier and linked the missions to Operation Shader, the UK contribution to the Global Coalition against Daesh, and to U.S. Operation Inherent Resolve.
The F-35B role in this conflict was carrier-based airpower: operational sorties, counter-ISIS missions, protective overwatch, and air strikes against Daesh. CJTF-OIR identifies Operation Shader as the United Kingdom's military contribution to Combined Joint Task Force - Operation Inherent Resolve, including kinetic airstrikes in Iraq and Syria, ISR, air-to-air refuelling, transport support, and partner-force training.
The public sources support UK and U.S. coalition use of the F-35B from HMS Queen Elizabeth during the continuing anti-ISIS campaign, but they do not provide a public target-by-target strike list for the F-35B sorties. The safest conflict-use summary is therefore that UK and U.S. F-35Bs were fielded from HMS Queen Elizabeth for combat missions, counter-ISIS sorties, protective overwatch, and reported air strikes against Daesh in support of Operation Shader and Operation Inherent Resolve.
Sources: Stealth jets fight Daesh in first combat missions from HMS Queen Elizabeth, U.S. Marine Corps Squadron Supports Operation Inherent Resolve from Royal Navy's HMS Queen Elizabeth, UNITED KINGDOM - Operation Inherent Resolve Coalition, US Marine Corps depart Carrier Strike Group