I can't really offer a reliable estimate of pheasants released in the UK nor can I comment on their involvement in Lyme disease. However it is certainly a huge number. The BIG shoots put down 10's of thousands of birds each and in certain areas of the country there are quite a few BIG shoots. Some on these shoots offer 2-400 bird days several days each week from late October to the end of January. Working on an average of 300 birds/3 days per week/12 week season = nearly 11000 birds killed and a 40% return on birds put down would give a total of roughly 25000. And that is one shoot. My local estate that shot 6 days in the reason and only 80-120 bird days put down 500 partridges and 1000 pheasants. And that doesn't include wild bred birds.
Comparing to Iowa isn't helpful because you have bag limits, we don't!
I don't doubt the 50 million is an exaggeration but the real number is still staggering.
Now that everybody has to register if they keep even one bird in confinement (because of bird flue), it should be easy enough to establish the real numbers if you could be bothered.