It's a little complicated with all the carriers and products... AC Tango is not really the same as LH Light or UA Basic Economy. It looks like AC has realigned their names, and an X class ticket should be "Economy Standard" and not "Economy Basic" (includes a checked bag TATL, but not within North America, as would be standard for a discount Economy fare). Similarly, with LH Group carriers, X is Economy Classic, instead of Economy Light, and should include the legacy standard bag allowance (but not whatever the Flex/full fare allowance might be). Also, it's worth noting that most LH Group carriers permit zero free bags on a Basic fare even if you are *G. LH proper is still allowing it "as a temporary courtesy" last I read their website, but they've added a loophole to the alliance rules about the baggage benefit to exempt zero-bag fares, and it's clear they're going to drop the courtesy soon.

Now, some of my knowledge here could be out of date since this has been changing a lot recently, but if TATL Economy awards stop having free baggage I think we would have heard more.