Agreed with what y'all say above. But I'm pretty sure that if you do get an amendment, it will read something like that, and it could ironically limit later civil rights legislation even if the clarifying phrase is thrown in.
On the other hand, I'm not sure an amendment is likely. Americans of that time were mostly fine with the courts striking down "unreasonable" economic legislation, they just disagreed about what was and what wasn't unreasonable. So if you do get an amendment, you might get an alternative amendment saying something like "Nothing in this Constitution shall be interpreted to prohibit reasonable economic legislation." While it would rightly be seen as a shot across the Supreme Court's bows (and will probably lead to some loosening of the Lochner era rulings) in the long run, ironically, the this amendment would enshrine some of the basic Lochner principles into the Constitution more than OTL.
Also, as far as civil rights go, remember that the Lochner rules sometimes had a pro-civil rights effect. Going after unions, e.g., helped blacks since the unions were often whites-only.