Interesting problem, Tlat. I've been thinking of the following possible scenario. Imagine alt-Clark, whose parents are dead. Also imagine that he hasn't yet met our Lois, so that he has not revealed to the world that Clark is Superman. Now have him go out into space to fight Nightfall, and he'll end up suffering from amnesia, probably because of his violent crash landing on the Earth. He would get up, totally disoriented. His suit would be badly torn and singed, and he could just get rid of it somewhere. He would get back to his own apartment and fall asleep there. In the morning he would know that he is Clark Kent, but he would have no idea that he is also Superman.
Meanwhile, Lois could be in the Congo, captured and very ill treated, so that she suffers from a complete mental breakdown. She is rescued and brought to a hospital. A doctor there - Doctor Deeter? - falls in love with her. He persuades his colleagues that the best way to treat Lois Lane will be to make her forget everything that has happened to her, and to give her a completely new identity. Somewhat reluctantly, the others agree, and Doctor Deeter takes Lois away. He brainwashes her into thinking that she is another person altogether. He tells her the made-up story of her life, and he has at least one accomplice (possibly more) who agrees with him and feeds Lois the same lies. She becomes convinced that she is somebody else, that she has had another life altogether, and she probably even believes that she and Doctor Deeter belong together. Perhaps she marries him.
How would she and Clark meet? It would be interesting to have Clark unconsciously suppress his own powers, so that he honestly wouldn't know that he is Superman. But he is a reporter. Perhaps he would be sent somewhere to write a story? Perhaps he would meet Lois there? Alternatively, perhaps Lois is unhappy with Doctor Deeter, so that she would try to investigate something just because she feels the urge to do something like that? And perhaps something in her investigation would bring her into contact with Clark?
Remember that if we are talking about alt-Lois, there is already an established amnesiac version of her, called Wanda Detroit. Luthor uses her amnesia, which I believe she got one way or the other in the Congo, and he tells her that she is called Wanda Detroit, and that she is a night club singer. Luthor would almost certainly bring "Wanda Detroit" to Metropolis, and Clark could meet her there during an investigation.
And how do you stimulate their memories? My suggestion would be to just let the famous Lois and Clark attraction work its magic. Clark, at least, would be extremely attracted to Wanda, and I think he would somehow sense that there was something wrong with her. He would discreetly try to find out more about her, and he would definitely discover that Luthor was very much involved in her life. As Clark would distrust Luthor, he would try to dig deeper and find out more about "Wanda Detroit". He might indeed trace her to the Congo, and possibly even learn that her name is Lois Lane. He could try to meet her and tell her what he has learnt about her. As for Clark, well, he might accidentally discover a super-ability of his. As a reporter, he would know about Superman, so he would have to wonder about a possible connection between himself and Superman.
Wow, Tlat, that was a lot. Well, just a thought, you know.
Good luck with your story!
Ann