Turing's 1937 paper (of just one page!) which defines $Theta$, his own fixed point combinator, refers to a 1936 paper by Kleene in which a "function L with a property similar to the essential property of $Theta$" is defined.
References:
A M Turing, The P function in $lambda$-K conversion, Journal of Symbolic Logic Vol 4 No 2 December 1937 p. 164
S C Kleene, $lambda$ definability and recursiveness, Duke Mathematical Journal, Vol 2 1936 p. 346
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