What this sounds like is you have NOT reset your phone to factory settings after the initial settling in of JB. Please do the following:
1. Save your photos and files you want to keep on your computer.
2. Do a factory reset of the phone and DO NOT SAVE ANYTHING.
3. Delete all memory cards etc....to get rid of old versions of apps that might not be compatible with JB.
4. When you come back up, the phone will ask you if you want to restore what they saved in your back up files...the answer is NO. Even if you are putting the same email addresses on your phone, please say NO!
5. Fill out the required information and bring the phone back up.
6. BEFORE adding anything to the phone...apps etc....you can put your photos and documents back on, but don't install an app for at least 24 hours. Let the phone settle in.
7. Read this forum and follow instructions of other members on how to get around the keyboard issues...example chrome problem with shift key. Because you will have that still.
This should fix your lagging issues....then after 24 hours you can start adding your apps back....JB is not too bad, once you get the first set of bugs out and let the phone settle in.