What meter did you use? Lactose normally does not show up on the system used by One Touch (which reads only glucose)... but it may read on Abbott's system, as a high. Free and easy system may read other sugars, and that can be confusing.
But this does not explain a LOW in any way.

A reading of 40 is alarming....but one cannot depend on home monitors to be accurate that low. If the strips are not fresh, or you had not checked the calibration with the test solution recently, you can not rely on that reading.
When working optimally home units vary by 10pts or more per reading!

You would need a 4 hr (a 6hr would be ideal but most people cannot tolerate one this long) glucose tolerance test with accurate testing every 1/2 hr to see if and where you hit those lows.
Reactive lows may come from insulin resistance. A test for fasting insulin will show a high out of range if you have this. Too much insulin will clear the blood rapidly and cause reactive lows. This can be due to insulinoma tumors of the pancreas (not common), or the hypoglycemia illustrates an impaired glucose tolerance situation, which is a prelude to later diabetes in some people.

I think it is terrible that a reading of 40 was not followed up on by a doctor. Lows this low can cause unconsiousness, and even brain damage. (new studies on diabetics who gets lows like this show ONE low can lead to dementia!).