Actually, Ludendorff lost two stepsons
, both pilots, during the war. They were both sons of his wife, Margarethe. The eldest was Franz Pernet, a pilot with Jasta Boelcke
; he was killed in action on 5 September 1917, shot down into the sea by 2/Lt Keith R. Park (yes, the Battle of Britain Park) and 2/AM H. Lindfield of No 48 Sqn (Bristol Fighters). Franz was 22 years old and had flown with Fl Abt. 14. I don't believe his body was ever recovered.
On 22 March 1918, Ludendorff's second stepson died, and this is the one you're after. He was Ltn Erich Pernet, the 20-year-old pilot of an LVG C.V (apparently) from Fl. Abt. 29; his observer was Ltn. Karl Westphal. They were shot down by Camels of No. 73 Sqn, specifically Capt. Thomas S. Sharpe, and fell to earth northeast of Nesle. Sharpe would himself be shot down and captured only five days later, apparently as the 71st victory of MvR himself.
According to a book by German artilleryman Herbert Sulzbach, "With the German Guns," it was Sulzbach who found the wreckage of the LVG and recognized Erich's body as Ludendorff's son by the unit patch on his sleeve. There had been a notice put out to all front line units to search for the wreck of the plane and the airmen. Sulzbach claimed he received a telegram of thanks from Ludendorff himself, for finding the second of his two stepsons so that Erich, at least, could have a proper burial.
You can find out a bit more about Franz Pernet in Norman Frank's superb book "Jasta Boelcke", or in my upcoming little volume from Osprey on the same subject.