Is my answer to my manager, who does not fast, that "it's none of my business, and fasting is for Allah, between Allah and His servant" considered a lie or an encouragement to sin, especially since he asked me if I was bothered by his not fasting?

Intentionally breaking the fast during Ramadan (definition) without a valid Shar’i excuse is a major sin and a grave transgression. The matter worsens if done openly, as it constitutes public defiance and wounds the feelings of those who are fasting. Whoever witnesses such an act should advise the doer in the best manner.