I first heard of this story at work some years ago.
A columnist relates the episode here:
The Rio Grande Valley along the Texas and Mexican border was known as the region where votes could be bought. Most close elections were decided in these counties, which would come in days after the original count with just the right number of votes needed to win the election. This is how Johnson won by only 87 votes in a race where over one million votes were cast.
Johnson became known as Landslide Lyndon in Washington because of this 87 vote victory. It was also an allusion to how he had stolen the seat. Some people think that Johnson’s title, Landslide Lyndon, stemmed from his landslide victory over Barry Goldwater in the 1964 Presidential Race, but it was actually from the 1948 Texas Senate Race.
A legendary tale that is attributed to Johnson in this infamous race claims that in the days following the election, while garnering enough votes for victory, Johnson and the political bosses of the Valley counties were going through cemeteries and taking names of dead Mexicans off of tombstones to register as voters. They could not decipher one of the names and asked Lyndon what to do. Johnson quickly replied, give him a name, he’s got as much right to vote as the rest of them in this cemetery do.