An interesting puzzle.

Your information on Lewis is correct, and a reading of his obituary reveals that he does not seem to have had any relatives with this specialism, and in fact stumbled into the study of the Turkish language while at university in 1939 as a result of his Latin tutor's suggestion that he needed a new hobby – so it's not as though he was the son of a long line of Turkic experts named Geoffrey Lewis.

I then turned to look at the series in which Lewis's book appeared. This check revealed an interesting point, which is that the Lewis book is not the only one to exhibit the anomaly you have identified. H.L. Williamson's Teach Yourself Chinese is listed as "First printed 1923", which is before the book's actual initial publication date of 1947, and of course also before English Universities Press commenced trading. Similarly, M.B. Lewis's Teach Yourself Malay is listed as "first printed 1917," although it actually first appeared in 1947. And one edition of A.S. Tritton's Teach Yourself Arabic is listed as "first printed in 1913", although it actually first appeared in 1943, and another edition of the same book correctly gives 1943 as the "First printed" date .

A more solid clue as to what is probably going on here appears in the Teach Yourself German title, which is attributed to Sir John Adams, Sydney W. Wells and E.S. Jenkins, and first appeared in 1938. This was four years after the death of Adams, and also 37 years after he published his book Self-Education in German (1901). The explanation for this anomaly appears in the small print on the title page, which notes that the book "is based on the work by Sir John Adams, completely revised and enlarged" by Wells and Jenkins. The print data page for Teach Yourself German adds the work was "first printed in this form" in 1938.

It would appear, then, that the publishers of the Teach Yourself series at least sometimes commissioned works that were based on other, earlier works. The fact that Teach Yourself German acknowledges Adams' work further suggests this was, at least sometimes, the result of some formal arrangement with the publishers of the earlier works. On the whole, however, the precise mechanisms at work here remain something of a mystery, since similar admissions do not appear in the other books in the series I have examined, and in some instances there were in any case only a very few language guides of any sort in the relevant language available to the general reader before the Teach Yourself series produced one.

The best detail I have been able to find in this respect emerged as a result of pursuing the lead with regard to the Teach Yourself Chinese title. Here I turned up Nicola McLelland's history of Chinese self-instruction manuals, published in the Journal of the Chinese Language Teachers Association, which includes (p.10) a list of "all the very few self-instructional manuals of Mandarin Chinese available in the UK up until the 1970s". This not only shows no Teach Yourself Chinese book published in 1923, but reveals that the only title in remotely the correct field published between 1914 and 1947 was Colloquial Chinese (Northern) by one Neville J. Whymant – which appeared in 1922. There is no apparent link between Whymant – a lecturer in Chinese at the School of Oriental Studies in London – and Williamson, a Baptist missionary who was working in Shanxi between 1908 and 1926, and Colloquial Chinese (Northern) was part of a series of language books published by Kegan Paul, which also had French, German and Japanese titles and would appear to have been a rival imprint to the Hodder-owned English Universities Press.

Was there some association between Whymant's book and Williamson's? The former's name appears nowhere in the latter's, and the dates - Whymant's book appeared in 1922, Williamson's was "first printed" 1923 – don't coincide exactly. Similarly, I've been able to find no obvious precursor to Teach Yourself Arabic that appeared in 1913. A search of the British Library catalogue reveals two distant possibilities – Elias Elias's New Dictionary of English-Arabic and William Wortabet's Arabic-English Dictionary both appeared in that year – but Tritton mentions Elias only once, and Wortabet not at all, in the course of his book, and stresses that the most important Arabic grammar is actually William Wright's, which was published between 1859 and 1862.

I conclude that there is evidence that at least some of the books in the Teach Yourself series were based on earlier works, and that if something of this sort had happened in the case of Teach Yourself Turkish, it would be a plausible explanation for the anomaly you have spotted. But, unfortunately, although I checked the British Library catalogue for works published in 1919 with the word "Turkish" in the title, my search was without result. So I can't point to a smoking gun in the case of Lewis's book, and my research into Williamson's suggests that, no matter what the claim to a publication date of 1923, there's no obvious link between that book and any teach-yourself-Chinese type title that actually appeared in that year.