Many years ago I had a burst appendix in Yemen, of all places. The Swissair (SR not LX) representative in country arranged an evacuation via ATH to both ZRH and LHR, so my spouse could make the destination decision in ATH. I ended up in LHR with the best hotel, oops, hospital I had ever seen The Wellington, which had concierge service and a mini-suite so my wife could stay with me.
That made me very loyal to SR and determined to always have good international health/evacuation insurance. I have not had a claim on IHI but I have had occasion to seek their advice, which is excellent, and a close friend was evacuated from the Sudan by them with superb service. I cannot recommend them highly enough.
http://www.ihi.com/