***NOT A TEACHER***diegoami, good afternoon. What a great question. As a native speaker, I am ashamed that I cannot give you an answer with 100% confidence. All I can do is offer a few points until you get a better answer: (1) Well, "lied" is, of course, wrong. "Lied" is the past tense of "to lie" (not tell the truth). (2) Maybe (maybe!!!) "If the guy lay down, he might survive" is grammatically correct. (3) I DO know that many Americans refuse to use "lay" for the past tense of "to lie" (be on your back). Many Americans say, "Yesterday I laid on the beach." (Of course, "laid" is the past of "to lay" (put something). (4) I cannot prove it, but maybe "lay" sounds "strange" to Americans because they are so used to the past ending in an -ed sound. (5) By the way, I linked to that comic strip that you saw. Of course, if you were describing what happened, you would have said: Sadly, the guy died when the train hit him. If he had lain down, he would have survived because the train would have passed over him. (6) That's all I can offer. Let's see whether someone can explain to you -- and me -- why "If he lay down, he might survive" is "wrong." Have a nice day.
Is the following sentence correct ?
If the black guy lay down, he might survive.
or should it be
If the black guy lied down, he might survive.
Your sentence is correct.
Your conditional sentence would be: If the black guy lay down, he would survive. If it's not completely certain that he would survive, you can say: If the black guy lay down, he might survive. - as you have.
For 'lie' = mentire: lie/lied/lied