Share your experience!
Try this
settings > apps > all > phone > clear data > restart the phone
if that doen't help, backup your texts and then open the messaging app and delete all conversations
How to backup
Alternatives on How to backup Xperias
http://talk.sonymobile.com/thread/36355
Where do you experience the scrolling lag?
Try my above suggestions and report back.
Also clear the app data on google chrome
I forgot to ask, do you have an antivirus or taskiller app(s)?
uninstall them > restart the phone > check again bc those apps aside of draining your battery they will create this issues.
Sounds good, keep us updated.