Can i use my auto battery to jump start my vespa lx150 scooter without damage to either?

If both systems have the same voltage rating, and if you do the connections in the right order there will not be any problem. It is not physically possible to damage your car or you bike, or your batteries, or your starter, or your whatever... Where do you guys get off making .... up!!

No!

The juice from a car will likely cause damage to the gel packs(battery) they use in modern vespas.

I ride a motorcycle and I tried it. It fried my batterie's gel packs.

the simplest answer to give with the minimal info provided would be:
Check the voltage ratings on the batteries.
Chances are your vespa's a 6 volt system and the car battery will be 12, making them incompatable. You may get away with it once or twice but believe me you WILL do damage.

If you do use a car battery to jump start do it quick and without the car running. After prolong use of doing this it will damage the electrical and starter on your bike.

It would be best to invest in a Battery Charger from your area Auto Zone or Pep Boys. Or, take your battery to a shop to have it charged. Jump starting from your automobile would cause extensive damage to your bike, it could cause your electrical system to short out. You would know it when you smell a burning scent or actually see smoke. If you don't have a shop near by to purchase or get your battery serviced, you could purchase one from "Parts for Scooters" on-line. You can jump start the bike from your auto battery, but be sure that you know what you are doing. If you don't know what you are doing, I still recommend a Charger or a Jump box.

yes i have done it.