The Lemegeton survives in manuscript, not in an early printed edition, and the manuscripts are the only evidence for what it originally contained.
The principal witnesses are in the British Library. Sloane 3825 is a seventeenth-century copy and is the manuscript from which the standard modern edition takes its base text. Sloane 3648 is dated to around 1665 or later. Sloane 3805 is dated 1685. Harley 6483 was written in 1712 and 1713. Sloane 2731 carries the date 1572, which would be extraordinary if it could be sustained, but the manuscript is generally read as considerably later, 1687 has been proposed, and the earlier date is not accepted. Further copies exist elsewhere, including one at Northwestern University from 1713 and a Wellcome manuscript finished on the first of March 1828.
Internal evidence narrows the window further. The date 1641 occurs in the text, so the section containing it cannot be earlier. The work draws on printed books whose dates are known: editions of Turner from the 1650s and 1660s, Saunders from 1671, and the 1665 Scot which is the demonstrated ancestor of the Goetia's catalogue.
Taken together this places the compilation in the second half of the seventeenth century, with parts of it demonstrably later than 1665 and the surviving copies running from then into the nineteenth century.
There is no known compiler. No manuscript names one, no contemporary source attributes the work to anyone, and the internal evidence of borrowing from several unrelated printed books points to assembly rather than authorship. Whether one hand assembled all five parts or the collection accreted is not established, and both positions have been argued.