Here are a few candidates, depending on your criteria:
* Robert Cawdrey (1604): Published *A Table Alphabeticall of Hard Words*, considered the first English dictionary. It focused on obscure or difficult words, not the whole language.
* John Minsheu (1617): Published *The Guide into the Tongues*, a comprehensive dictionary, but it was primarily Latin-English.
* Henry Cockeram (1623): Published *The English Dictionarie*, a more comprehensive English dictionary, still focusing on obscure words.
* Thomas Blount (1656): Published *Glossographia: or, A Dictionary Interpreting the Hard Words of Whatever Language, Now Used in Our English Tongue*, one of the first dictionaries to include slang and technical terms.
Ultimately, the "first lexicographer" title is debatable. Cawdrey's *Table Alphabeticall* is often considered the earliest English dictionary, even if it wasn't comprehensive. However, Minsheu's work was more complete and influential for later lexicographers.
It's important to remember that the concept of a dictionary was evolving during this time, and these early works paved the way for the comprehensive dictionaries we know today.