By no means a comprehensive list, but here are some works that I have read:
A Tutor for the Renaissance Lute by Diana Poulton
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The Lutenist’s Handbook: A Practical Rough Guide to Playing Renaissance Lute by Ben Salfield
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Study of the Lute by Ernst Gottlieb Baron (1727)
Translated by Douglas Alton Smith
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Historical Lute Construction by Robert Lundberg
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A History of the Lute from Antiquity to the Renaissance by Douglas Alton Smith
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The Lute in Britain: A History of the Instrument and Its Music by Matthew Spring
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These are the best sources of lute instruction material and related literature that I have discovered so far:
Physical books:
The Lute Society catalogue and other publications
The Lute Society of America books
Early Music Shop books
The Lute Stuff website books
Lark in the Morning books
Online digital books:
Tree Edition library
University of Cambridge Digital Library
Casey Fitzpatrick’s manuscript library
If you aren’t sure where to start, this site has compiled a list of the 20 best lute books https://www.cmuse.org/best-lute-book/