The General American pronunciation of lox is /lɑks/ [1], the Standard German pronunciation of Lachs is /laks/ [2]. Those vowels are not the same; the American one is further back. In other dialects of English, it would also be rounded and/or less open.
And the dictionary of the Swiss German language (which in many ways resembles Yiddish more than Standard German does), says that the spelling used to be "Lächs", which probably means that the vowel used to be brighter than it is today: https://digital.idiotikon.ch/idtkn/id3.htm#!page/31041/mode/...
The letter changed, but the pronunciation didn't - hence "not changed in sound". German "a" == English (short) "o".