You can keep checking back on your question to see if anyone else gives a different or better answer but here goes my answer.
Lupus is an autoimmune disease and much research points to the cause being a Vitamin D deficiency. So in general taking Vitamin D helps in any autoimmune disease. Vitamin D has a big effect on the immune system. Did you happen to read http://www.vitamindcouncil.org/health-conditions/systemic-lupus-erythematosus/. I looked quickly for a specific mention of neutrophil increase after taking Vitamin D but could not find anything. It does not mean though it does not happen.
I hope you have had your Vitamin D levels checked and are taking Vitamin D. Minimum level we promote is 50ng/ml. The minimum amount of Vitamin D we recommend is 5000 iu but the upper limit of safe is 10,000 iu. If you already have a disease you may use up Vitamin D faster or need more than someone that is healthy.
Here is a story! Several years ago my 18 year old banged her head really hard at work. The next day she had a fever. Not knowing if the two were connected, we took her to the emergency room. Well they did their usually blood work and such and were almost ready to send us home. Results came back saying she had a very low neutrophil count. She was admitted. They did all sorts of tests, could find nothing and said sometimes viruses can cause this. Until her count came up though, she could not leave. In the mean time we had stopped her Vitamin D supplements for those first several days. When they could find nothing wrong, I realized unless we started the Vitamin D again she would probably be in the hospital quite a while.(She felt fine.) So we did not tell anyone and restarted the supplements. Low and behold the count started to increase the next day and we left two days later. A coincidence? I don’t think so!