I'm sorry you have ILC. I did too but mine had grown to 10cm or about 4 inches. I was pre-menopausal at 52 when I got mine and didn't achieve menopause until late last year and I'll be 55 shortly.
I don't blame you for not wanting a mastectomy. I didn't want one either but it was either a mastectomy or breast tissue that was trying to kill me. ILC is mostly estrogen driven. Though you may not get your period any longer, that doesn't mean you are menopausal or that you are not producing estrogen since body fat and the adrenals produce estrogen too. I also removed my other breast (because ILC tends to go bilateral) and had immediate DIEP reconstruction using my stomach tissue and it's blood supply but leaving the muscle intact. I love my breast-tissue-free breasts! If you go and have the mastectomies at a place that does immediate DIEP reconstruction you will have minimal scars on your chest and will wake up with breasts and your own skin and depending on where the cancer is in your breast, you could potentially even spare your nipples.
Anyways, once a cancer gets to a certain size or is located too close to an excisional margin they will do mastectomy. Consider that this cancer can come back again in the remaining breast tissue. It's not wise to leave it there. Take your time and research. Here is a link to a post I made about ILC for someone else and it gives you a lot of information to consider. Research, research and research some more!
http://www.medhelp.org/posts/Breast-Cancer/ilc/show/1324025
Best wishes. Psssst... your profile says you're a male. FYI