What is called the Lambda algebra ($\Lambda$-algebra) in stable homotopy theory is a differential graded algebra over $\mathbb{F}_2$ whose chain homology is the second page of the classical Adams spectral sequence.
It has the advantage over the May spectral sequence that it tends to make the extension problem for the Adams spectral sequence more tractable (Kochman 96, corollary 5.2.8)
The construction originates in
See also
Textbook accounts include
Doug Ravenel, section 3.3 of Complex cobordism and stable homotopy groups of spheres 1986/2003
Stanley Kochman, section 5.2 of Bordism, Stable Homotopy and Adams Spectral Sequences, AMS 1996
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