Unfortunately dotted line aren't, natively, supported in Tabluea, with the exception of Trend and Reference Lines. There is a work around (Eddie Van Halen and Dashed Lines | Drawing with Numbers or Dashed Lines in tableau) although it does require some reshaping of data. My suggestion would be, instead of using a dual axis, use a reference line.
If you look at the attached, I've dragged Profit into the Detail Shelf. This gives me access to it in the Reference lines (which you can control to be dotted). It only really works for a straight line (if for example you wanted to use it by Cell, it will create a series of 'steps', and not a continuous line, so you'd need the solution above from drawing with numbers) .
I hope this helps, and this is on the ideas board ((http://community.tableau.com/ideas/1378) so you could vote it up!
Dotted Lines.twbx 401.9 KB