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I have consolidated a half dozen threads going back to this time last year to illustrate that targeted offers without the once-in-a-lifetime provision are not rare, and are valid as written. Once-in-a-lifetime isn't an American Express policy, it's a shorthand summary of a restriction which appears is most offers. If it's not there it doesn't apply, just be sure to document the terms.
Also, bear in mind that lifetime is an exaggeration. The lookback period is about seven years.