There are certainly occurrences of "anlysis" much earlier than the 1970s, but these look to me like either typos or a degree of illiteracy. For example, this 1914 agriculture bulletin:
The selection of samples for chemical anlysis is more important in
obtaining true results than is the chemical anlysis itself. Portions
of the Feed to be analyzed should be taken from as many sacks as
convenient and thoroughly mixed and ...
Note that in the above extract, "analyzed" retains the correct spelling.
Further evidence to suggest that the spelling is an error or aberration can be found using Google Ngrams, which shows that this "anlysis" spelling has never represented more than about one ten-thousandth of the usage:
The etymology of the word doesn't seem to have a "missing-a" branch. ODO gives this origin of the word:
Late 16th century: via medieval Latin from Greek analusis, from
analuein 'unloose', from ana- 'up' + luein 'loosen'.
Etymonline provides the following:
1580s, "resolution of anything complex into simple elements" (opposite
of synthesis), from Medieval Latin analysis (15c.), from Greek
analysis "a breaking up, a loosening, releasing," noun of action from
analyein "unloose, release, set free; to loose a ship from its
moorings," in Aristotle, "to analyze," from ana "up, throughout" (see
ana-) + lysis "a loosening," from lyein "to unfasten" (see lose).
Psychological sense is from 1890. Phrase in the final (or last)
analysis (1844), translates French en dernière analyse.
It should also be noted that if you're reading an electronic version of any document from the 1970s or earlier, there's a risk that the OCR software that turned it from a printed image into text may have misread the word, and it hasn't been corrected.
TL;DR: There's no evidence that anlysis was a widely accepted spelling, and no evidence that there's any etymological basis for that spelling.