Broadly speaking, you can only create an alert for something that changes over time. Usually, reference lines are static, so there is nothing that Tableau can use as a trigger to send an alert. (There is more to it than that, but that will do for this discussion.)
It sounds like you're trying to do something like "send an alert when the value of this measure exceeds the value of this reference line". Is that right?
Yes Michael. I am looking for the same.
OK, so create your alert based on the actual measure that will change, not on the reference line.
I would be surprised if that worked on a Gantt chart view, but maybe it's possible. I'd try to get it working on a simple viz first so that you understand the principle, then attempt it with a more complex viz.