You're citing information from two different studies that could very well have used different methods for counting lemmas. The text in between the two bits you quoted illustrates the extent to which this is the case: Alongside your study of 20-year-olds finding that they recognize ~42,000 lemmas, there's an earlier study of people about the same age finding that they recognize between 12,000 and 17,000.

The magnitude of that difference (250-300%!) should serve as a stark illustration of just how hazy these estimates are, even within a language.

Between languages, it gets even more difficult. It's very hard, possibly impossible, to come up with a single standard for what counts as a word that doesn't favor one language over another. For example, I wouldn't be surprised if you could engineer a comparison that says that English has more words, and also one that says that German does, simply by changing how you deal with agglutination. Or, if not that, then certainly agglutination and polysemy together.

Hm, that was supposed to be the total count, not for single speakers.

Checking for myself my information seems to have been wrong. As we say here, I take everything back and claim the opposite.. That will teach me not to check my facts I hope.

Hm, I also seem to remember that German has a thinner dictionary. I suspect that lemmas in German are difficult to count, as there are so many compound words. Apart from the joy of teasing fellow Britons for their stupidity, I don't see why an average German adult should recognise 40% more lemmas when the languages are so related.