The update to 10.1.1 will show up under the Update tab in the Mac App Store if...
1) You are signed into the Mac App Store using the same Apple ID you used to purchase Logic pro X in the first place.. If not... sign out using the menu option Store/Sign Out and then sign in again with the correct Apple ID
2) Your Logic Pro X app is named as such (and nothing else) and is located in the Applications folder..
3) Your Mac meets the minimum OS X specs for the update to 10.1.x which currently is OS X 10.9.5 or higher/Yosemite
Note: To confirm you are using the correct Apple ID, look under the Purchase Tab for Logic Pro in the Mac App Store app... It should be listed there.. If not, you are likely signed in under a different Apple ID than was used to purchase LPX.. If it's not listed there check the email receipt Apple sent you when you bought LPX for the correct Apple ID.
Failing that contact Apple directly for assistance... Id have a copy of your bank statement/CC Statement showing payment to Apple for the app..so they can track it down in their system,
http://www.apple.com/contact/