As Thomas Lumley asserted, Neyman and Pearson in $\rm [I]$ didn't mention lemma. They frequently used the word principle, basis while deducing the critical regions in various cases.
When was the first time it was marked as a lemma?
$\bullet$ Wilks in his book did outline the theory but again refrained from calling it as lemma.
$\bullet$ Cramér in his book never mentioned any lemma but explained the "basic idea of Neyman-Pearson theory".
$\bullet$ Lehmann termed it while "formaliz[ing] in the following theorem, the fundamental lemma of Neyman and Pearson".
$\bullet$ Kendall & Stuart did use the term while writing "the examples we have given so far of the use of the Neyman-Pearson Lemma ..." the "lemma due to Neyman and Pearson ..."
$\bullet$ In $\rm [VI],$ the authors detailed a Lemma, which would be the more familiar Generalized NP Lemma we are acquainted with.
Again with absolute certainty, I cannot ascertain whether this was the first time the word was introduced. But as of now, it seems.
$\rm [I]$ Neyman, J., & Pearson, E. S. ($1933$). On the Problem of the Most Efficient Tests of Statistical Hypotheses. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, $231(694-706), ~289–337.$ doi:10.1098/rsta.1933.0009
$\rm [II]$ Mathematical Statistics, S. S. Wilks, Princeton
University Press, $1943,$ sec. $7.3,$ p. $152.$
$\rm [III]$ Mathematical Methods of Satistics, Harald Cramér, Princeton
University Press, $1946,$ sec. $35.1,$ p. $527.$
$\rm [IV]$ Testing Statistical Hypotheses, E. L. Lehmann, John Wiley & Sons, $1959,$ sec. $3.2, $ p. $64.$
$\rm [V]$ The Advanced Theory of Statistics: Inference and Relationship, Maurice G. Kendall, Alan Stuart, Hafner Publishing Company, $1961,$ sec. $22.10,$ p. $166.$
$\rm [VI]$ Statistical Research Memoirs: Volume $1,$ University College, London, Department of Statistics, $1936,$ p. $11.$