Gilderoy Lockhart is not a Death Eather !
All of you remember the charming yet silly teacher for Defense against Dark Arts : he was beyond contest the most vain professor that Hogwarts ever welcomed. Only Hermione and Mrs Weasley seemed to find him some redeeming qualities and were the only ones defending him while the Harry and the rest of the Weasley family thought him incompetent and unable to teach while occupying this important role he had to fill in the wizardry school.
Then, considering how totally unfit he was, why did Dumbldore chose Professor Lockhart in the first place? According to WizardsandWhatsnot there can be but one reason : he could never have been a Death Eater and thus presented no threat to Harry and his friends unlike Professor Quirell ! Why this seems a bit candid it certainly could explain how Professor Lockhart landed in Hogwarts !
Cover picture from Imgur