You need to do what makes you comfortable and establish your boundaries in a clear way. Forget about any temporary awkwardness you might feel at the very occasional contact. After all, his behavior doesn't demonstrate he respects you very much.
1) He emails you twice--you defer a meeting using an ambiguous message that many folks might see as the polite brush-off. He's offered, you've hinted that you'll initiate any future contact between you. It's an appropriate response, and you've tried to create a comfortable atmosphere that preserves the appearance of polite acquaintances.
2) He phones--thus upping the stakes. He's trying to manipulate you into responding to him. Enough time hasn't elapsed for your busy work situation to have resolved, so he has chosen not to listen to your "no" as "no." Whatever his intentions may be in asking you to lunch, he clearly doesn't respect the priorities and boundaries you have set.
3) He emails AGAIN--which again demonstrates he doesn't respect your decision (unless on the off chance this email is an apology that doesn't include another attempt to meet with you).
Now, maybe this guy doesn't realize he's being disrespectful or violating the boundaries you're trying to set--maybe he's socially awkward, or naive, or simply eager to re-establish ties. Doesn't matter. The point is, his actions, and thus he, makes you uncomfortable. So you have a right to respond in ways that makes it clear his behavior is unacceptable.
Now, whether you tell your DH about it...well, I can't say what your relationship is like. Personally, in my job and its social demands I experience many "boundary issues" that I don't tell DH about. I just shut them down quickly and definitively. However, on the rare occasion that a particular person persists, I make sure DH knows about the situation. In your case, I'm not quite convinced that the situation has gone far enough to tell your DH--and a lot might depend on this most recent email and how often you're going to see "reunion stalker."