You can check-in your baggage in BSL to your final destination (if op by LX) at the SBB baggage counter for a fee of CHF 22.- / per piece the evening before. If you want an express delivery you will pay CHF 52.- per piece. But you need to register your baggage far in advance, your connection listen will not be possible for rail-fly-express baggage. You will find all your information here: https://www.sbb.ch/de/bahnhof-servic...k-express.html

Baggage check-in at Basel on the airtrain is no befefit, LX offers for free for it's customers.