If you did the backup of your notes before losing or deleting then you can easily get the lost/deleted iPhone notes back by the following steps:
1. First don't connect your iPhone directly to computer because the iTunes only saves the most recent backup
2. Now make sure that you have a valid backup as listed iTunes> preferences> devices
3. Before connecting your iPhone make sure to check iTunes>preferences> devices "prevent iPhone from syncing automatically." Because this will ensures we don't erase the previously stored backup. Then select "OK" and close the window after checking " don't sync"
4. Now connect your iPhone to your computer and run iPhone Data Recovery.
5. Select the iPhone as seen in the left bar of iTunes, as listed under the devices .
6. Select version and click on restore from options.
7. It takes a while to for iPhone to erase itself, reset and restart.
8. After the iPhone is restart you will see Set Up Your iPhone in iTunes on your computer, and now just click the restore from the backup and click continue. It will take 10 to 12 minutes to recover your deleted notes, photos, music, videos, etc.