Is it invasive lymph node metastasis is serious condition for breast cancer? Is it curable?

All forms. of breast cancer can be considered serious, but to answer your question, yes, breast cancer with lymph node involvement is potentially curable, but the probability depends on a number of factors. Survival rates are very high if the tumor is small and the lymph node involvement is minimal(stage 1B), and become worse with increasing tumor size, extent of node involvement, and distant metastases.
2nd defense. Lymph nodes are the 2nd line of defense against the spread of breast cancer after the 1st line, the immune system, lets some cells slip by. Many will have the cancer trapped for a while by the nodes, preventing the spread and removal of the nodes can be curative. If there is no evidence of the cancer elsewhere in the body, the nodes may have worked well. Check with your oncologist.