I read his letter about his party’s lifeboat capsizing and went looking for more information as that detail stood out as odd. It could have been collapsable A but his letter claims to see them off and then head stern before praying. Not much mention of how he got in a boat.
While it is possible that Thure Lundstrom was referring to Collapsible A (although it toppled sideways when the wave hit rather than capsize), there are several things that go against that conjecture. The main reason is that Lundstrom himself definitely survived; since we know that for certain, the question arises on which lifeboat.
If he had seen his fiancee Elida Olsson washed away when Collpasible A toppled sideways after being hit by the wave, that means that he was still on board the sinking
Titanic himself at that moment. If so, the only lifeboats that he could have reached to save himself were Lifeboat #4 (which picked-up Hemming) and the overturned Collapsible B. With so many women on board Lifeboat #4, any further rescue from the sea with or after Hemming would have been definitely recalled and mentioned; AFAIK, there was nothing like that and so we can rule out #4 as being Lundstrom's lifeboat. Most people in the vicinity of Collapsible A who later made it to #B - Gracie, Cecil Fitzpatrick etc - had probably gone to the port side
before the wave hit; Jack Thayer jumped into the sea with Milton Long but that was also moments before the wave arrived. Therefore, the only person who was still near Collapsible A when the wave hit but eventually survived on Collapsible B was John Collins. There is a small possibility that Lundstrom made it to Collapsible B but AFAIK no one else rescued on it said anything to support that conjecture.
Having said that, there is a tendency to place a surviving Scandinavian man whose lifeboat was uncertain in Lifeboat #15 simply because there were many Scandinavian men on board it. Thus, men like Karl Jonsson and Thure Lundstrom were thought to have been rescued on it, which is in fact quite possible. In that case, Lundstrom could have simply lost sight of his fiancee in the confusion or wrongly believed that she was already in another lifeboat. Later, riddled with survivor's guilt and mourning the loss of his beloved, he could have made-up the story that showed him in better light.