Biblical character, presidential predecessor of Andy J? (4)

I haven't cracked this one yet — but the brilliant team at Times for the Times have:

ABE Lincoln was President after Andrew Jackson, not his predecessor, (there were no Andrews before Jackson) so I’m not sure how “presidential predecessor of Andy” works, and L comes after J not before, so likewise; Andrew Jackson pre-deceased Lincoln (1845 and 1865) so we can’t use predecessor in the “died first” sense. Someone please explain what the setter had in mind here.