Is the problem with batteries or lithium batteries?
AirTags have non lithium batteries
AirTags have non lithium batteries
Both - when installed in a device - can be transported in checked luggage though: https://www.iata.org/contentassets/05e6d8742b0047259bf3a700b...
IATA actually has a document specifically addressing tracking devices: https://www.iata.org/contentassets/05e6d8742b0047259bf3a700b...
My reading of that document indicates that an AirTag should be fine, as low-powered wireless communication is allowed (page 9, item 3).
They are lithium primary cells though, not lithium ion cells, which are usually what is banned.
>[T]he CR2032 battery is a Lithium-manganese dioxide battery (LiMn02). It is composed of a Mn02 cathode and a lithium anode. The device is specified for a 225 milliamp hours (mAh) and typically operates over a temperature range of –20 ºC to +70 ºC.
You will find some alkaline versions available from some vendors, but it's not the norm.
Now there may be a chance that Lufthansa didn't mean to include all types of lithium cells or batteries, but the vague wording doesn't seem to suggest that.