Thanks for your question -
Patients that have had a lumpectomy can have altered sensation of the breast or nipple. The vast majority of the time that sensation should improve over time. It is possible that increased sensitivity could be permanent but that is rare.
Lidocaine injections aren't typically used to manage chronic sensitivity because the drug effect is short lived (typically 4-6 hours). Physical therapy can help with desensitization that doesn't improve with time.
I hope this helps.