Approx how long it takes for a lobular carcinoma cancer in situ becomes invasive?

No telling: One day to never (4/5 chance of never). This can't be predicted, any more than one can predict how long it will take for a couple to conceive. It is entirely a "playing the odds" decision. The key is to know that turning invasive isn't instantly-incurable, you have plenty of time to make the right decision for you about surgery, chemoprevention and/or intensive observation.

Unknown: Lobular carcinoma in-situ (lcis) is not cancer but a marker for the possible development of breast cancer in the future. You should speak with a oncologist who can run a risk profile and determine if you are a candidate for medications or surgery to decrease your risk.