That's what I would have assumed. But somewhere around here -- OK, on the first page of this thread, Bakerstreet Irregular quoted a short piece (this one: http://www.mayhematics.com/f/lestrade.htm ) in which an elderly Lestrade explains that his father and grandfather "always gave the name the Cockney pronunciation 'Lest-raid' rather than 'Le-strahd' as people educated in French tend to read it." The author is one G. P. Jellis, who I suspect to be the same individual who published a games journal
( https://www.cambridge.org/core/journals/mathematical-gazette/article/games-and-puzzles-journal-edited-and-published-by-g-p-jellis-99-bohemia-road-st-leonards-on-sea-tn37-6rs-5-for-6-successive-issues-issn-0267369-x/9E7298D9682DA0C615DE6679930084BF )
from a UK address, so I would assume s/he is correct about Cockneys using a different pronunciation. So I would consider that to be a definite possibility for how the "real" Inspector pronounced his name. But that's in the original Holmes universe. By the 21st century in the BBC Sherlock universe, Greg's family has apparently re-frenchified their name.