General reference works:

Renwick, W.L. English Literature 1789-1815. v. IX The Oxford History of English Literature. Oxford: Clarendon, 1963.
(Good overview.)

Tave, Stuart. The English Romantic Poets and Essayists: A Review of Research and Criticism, ed. Carolyn Washburn Houtchens and Lawrence Huston Houtchens. New York: MLA, 1957.
(Excellent summary of most criticism up to 1957)

Courtney, Winifred F. "Charles Lamb," Dictionary of Literary Biography. vol 93  of British Romantic Poets 1789-1832, First Series. ed. John R. Greenfield. Detroit, New York, London: Gale, 1990. (On Lamb's early work)

Courtney, Winifred F. "Charles Lamb," Dictionary of Literary Biography. vol 107  of British Romantic Poets 1789-1832, First Series. ed. John R. Greenfield. Detroit, New York, London: Gale, 1991. (On Lamb's  later work)

Articles:

Reiman, Donald H. "Thematic Unity in Lamb's Familiar Essays." JEGP 64 (1965): 470- 78. (the most important article on Lamb)

Tillotson, Geoffrey "The Historical Importance of Certain Essays of Elia.'" in  Some British Romantics. ed. By James V. Logan, John E. Jordan, and Northrop Frye. Ohio State UP 1966. pp. 89-116.

Mulcahy, Daniel J. "Charles Lamb: The Antithetical Manner and the Two Planes." SEL 3 (Autumn 1963): 517-42. (A groundbreaking study)

Books:

Barnett, George Leonard. Charles Lamb: The Evolution of Elia.  Indiana UP 1964.

Park, Roy, ed. Lamb as Critic. London: Routledge & Kegan Paul. 1980; U Nebraska P, 1980.

Lucas, E. V. Life of Charles Lamb. London: Macmillan, 1905.

Courtney, Winifred F. Young Charles Lamb: 1775-1802. New York: New York UP, 1982.
 

Note:
At present, there is not much room to provide more than this brief list here. Email me for information about a much more extensive bibliography which I can provide by email.