No, they're not "just lies, plain and simple." They MAY be lies but he may genuinely believe he ran 4 miles in 16:08 because that was the distance the race was advertised as. Obviously, he did not run 88 miles every Sunday while in high school. But he may have had a stretch where he did that for a while. If he was running for 11 hours I can see where he could have covered upwards of 80 miles. The 100 mile record then was around 12 hours and Lindgren was a much better runner than any of the ultra guys then. Cavin Woodward ran 11:38 for 100 miles in 1975 and reportedly maxed out at about 70 mpw, so Lindgren going a lot fewer miles in a little less time seems plausible, which is not the same as saying it happened.
Details matter. But you can also get so bogged down in minutiae that you don't see the whole picture. Lindgren was one of the best distance runners the US ever produced. He was one of the first who was truly competitive internationally. Simply dismissing his ideas as "lies" because you can't fathom someone doing what he says he did is as big a mistake as unquestioningly trying to imitate him.