Reporter William Kerns does a good job trying to fact-check the story, looking at the Beatles' tour dates for 1964 and 1965, when the visit supposedly occurred. The probability of the Beatles being able to make such a visit seems unlikely, yet Lana Dickson Townsend insists her father's story is true.
I don't recall any previous statements about this from the Beatles or anyone else. Certainly, the band loved Buddy Holly and were indebted to his inspiration as a performer and songwriter. But I find it hard to believe they'd make a special trip to do this. They weren't exactly sentimental types.
Anyway, here's a snippet of Kerns' article:
“It was either 1964 or 1965,” she said, when her late father, Jack Dickson, told her that four “hippie guys” arrived in disguise at his office. At that time, he was assistant manager of terminal operations for Continental Airlines.
...According to her father, the band had arrived in disguise, “wearing wigs, cutting up, joking with each other and talking very quickly.”
“He could not understand everything they said,” noted Townsend, “but he said they never stopped asking questions about Buddy Holly. They asked him if he knew Buddy Holly, which of course he didn’t. They asked him if he knew where Buddy Holly had lived, which of course he didn’t. And they’d flown in on a private plane, about an hour’s flight from Dallas, because they wanted to visit Buddy’s grave.
“I don’t know if it was my daddy or someone else who drove them out there (to City of Lubbock Cemetery). I just know daddy said that he was told to look after these men and to not let them leave his office.”