This has annoyed me since adolescence, when I became aware of it. As an American, I have noticed this phrase used almost universally (as opposed to "longue") in speech, and the majority of the time, in writing as well. High quality journalism sources (NY Times, etc.) or good quality (Time, Newsweek) almost always get it right.

As to your question about whether it will predominate, your guess is as good as anyone's. Keep up the good fight if you want, but you may lose in the end.

The "lounge" association seems so tempting, that no doubt you're correct about the origin of the mispronunciation and misspelling, but I don't know that for sure. As to what one can do about it, I think the answer is, not much. Normative efforts don't get you very far (not, for me, "don't get one very far") since the language will simply gallop on ahead and leave you in the dust. On the other hand, your use of the language may have just as much weight insofar as which way the word will be described in future dictionaries, so if you prefer "chaise longue" (as I do), by all means support it, by using it!

The topic of your comment could be generalized (not "-ised" as in the U.K.) to foreign loanwords and how English (or any language) deals with them. While the word stills seems "foreign" we tend to keep a semblance of the original pronunciation (to the extent that the sounds can be matched by a similar English phoneme), and sometimes put it in italics or in quotes. E.g., "laissez faire" is pronounced around here quite similarly to its pronunciation in French--no "z" sound, for example. On the other hand, "flamboyant" has been around a long time and we accept it as English, so it is pronounced "like an English word", 't' pronounced, emphasis no longer on the last syllable.

It would be interesting to look at a list of loanwords from French (or any other language) sorted in decreasing frequency from the common to the obscure, and see how we Anglophones would pronounce them.