*G is worth nothing on LH eco light flights. The limit for all passengers, including *G is 0 pcs.
On eco classic 1 pcs of baggage is included, and as *G you can take 2 pcs.
Eco classic fare can be book only on LH webpage or by TA, it is not possible on OTA.
Be careful - if you book eco light, and pay for additional luggage - the limit for *G is still only one pcs.