Dear Jo2, Lumpectomy is a possibility with infiltrating lobular cancer. Lobular cancer grows differently than ductal cancer, it grows with little fingerlike projections out into the surrounding tissue, these tumors tend to be larger. Like with ductal cancer negative margins would be obtained and it may be that a little more margin would be planned to be sure to leave clean margins. You would want to have a good discussion with your surgeon about your options, it may be that the amount of tissue that might be anticipated removing, as well as your breast size - a good cosmetic result might be difficult with lumpectomy, and mastectomy with reconstruction might be a better way to go.
I would not say that lumpectomy is "never" done with ILC. However, because ILC has more of a tendency toward multifocal locations -- meaning it can be in more than one spot in the same breast -- it was initially considered an exclusion for breast preservation. It can also be harder to detect early on a mammogram, because its pattern early on looks more like glandular tissue on xray. When one hears of a woman with a breast cancer and a "normal" mammogram, it's much more often a lobular cancer than a ductal one. So choosing breast preservation with lobular cancer must be done recognizing a need for extra vigilance; but I know of many women who choose it.
I too had a 5cm mass in left breast and the same treatment. My tumor shrunk to about 1cm, but my surgeon chose to do mastectomy anyway. After surgery, it was the right choice, due to fingerlike projection that grew from that tumor and microscopic cancer cells throughout my breast that didn't show on the ultra sound. Good luck to you whatever way you chose to go.