First of all, welcome to FT. Don't hesitate to start a new thread if needed...

I can't give you information on LX but LH has the biggest bassinets I know of. My year old baby fit in one on a transatlantic years ago and I understand they're still good. Most bassinets only hold little babies to about age 6 months.

There is no "gadget" you can get to make a lap baby safer. Some airlines use "belly belts" not for the baby's but for the other passengers' safety. They're provided by the airlines (not by U.S. and Canadian companies because of the risk to the child). The risk of anything going wrong is very slim so lap babies are allowed. It can be uncomfortable though as they grow.

I was able to quickly look it up. Not good news but typical in the industry.

We offer a baby-bassinette in all classes on long-haul flights and in Business Class on short-haul flights. It measures 70x30x20 cm and is suitable for babies up to the age of 8 months and weighing about 10 kg. It may be used during the cruise phase of the flight but not during take-off and landing.
http://blog.swiss.com/2011/10/travel...-children.html

If you bring a car seat, you may or may not score an empty seat to use it in. Both airlines will let you use it but unlogically, Swissair wont let you for take-off and landing (the most important times to use it!) Lufthansa will (experience with U.S. car seat speaking). If you are bringing a car seat to Israel, be sure to GATE check, not luggage check it so bring it to the gate either way. That way you'll be ready if a seat opens up. It's a real sanity-saver to have the baby in a separate seat!