I have invasive lobular carcinoma. What are my chances of complete recovery?

Good. Lobular breast cancer is more frequently multifocal and bilateral than ductal carcinoma. However, with mastectomy (lumpectomy may not be sufficient) and sentinel lymph node biopsy, with follow-up hormone therapy and/or radiation should yield a good outcome, depending on the grade and stage of the cancer. Stage is most important, along with hormone receptor status.
It depends. Your chance for cure or prognosis is primarily dependent on your stage of cancer rather than the type (lobular, ductal, etc.). The cancer stage is based on the status of your axillary (sentinel) lymph nodes, the size of the cancer, and tumor-specific factors such as estrogen receptor, Progesterone receptor, her2/neu receptor, tumor grade, oncotype-dx score, etc.